1986 documents matched the search for jumps in titles and keywords.
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Multi-jumps, Massimiliano Caporin, Aleksey Kolokolov and Roberto Renò,
from University Library of Munich, Germany
(2014)
Keywords: multi-jumps, co-jumps, price jumps, multivariate jumps, jumps testing
Internationally correlated jumps, Kuntara Pukthuanthong and Richard Roll,
from European Central Bank
(2012)
Keywords: Correlation, diversification, jumps
Volatility and return jumps in bitcoin, Pedro Chaim and Márcio Laurini,
in Economics Letters
(2018)
Keywords: Bitcoin; Cryptocurrencies; Stochastic volatility; Jumps;
The high-frequency impact of macroeconomic news on jumps and co-jumps in the cryptocurrency markets, Walid Ben Omrane, Khaled Guesmi, Qi Qianru and Samir Saadi,
in Annals of Operations Research
(2023)
Keywords: Macroeconomic news, Jumps, Co-jumps, Bitcoin, Ethereum, High frequency data
The dynamics of co-jumps, volatility and correlation, Adam Clements and Yin Liao,
from National Centre for Econometric Research
(2013)
Keywords: Realized volatility, correlation, jumps, co-jumps, point process
Price and volatility co-jumps, F.M. Bandi and Roberto Renò,
in Journal of Financial Economics
(2016)
Keywords: Stochastic volatility; Jumps in prices; Jumps in volatility; Co-jumps; Infinitesimal cross-moments; Return risk premia; Variance risk premia;
Do idiosyncratic jumps matter?, Nishad Kapadia and Morad Zekhnini,
in Journal of Financial Economics
(2019)
Keywords: Idiosyncratic jumps; Idiosyncratic risk; Limits to arbitrage;
Oil shocks and volatility jumps, Konstantinos Gkillas, Rangan Gupta and Mark Wohar,
in Review of Quantitative Finance and Accounting
(2020)
Keywords: S&P500, Volatility jumps, Oil shocks
Oil Shocks and Volatility Jumps, Konstantinos Gkillas (Gillas), Rangan Gupta and Mark Wohar,
from University of Pretoria, Department of Economics
(2018)
Keywords: S&P500, Volatility Jumps, Oil Shocks
Volatility Jumps, Viktor Todorov and George Tauchen,
from Duke University, Department of Economics
(2010)
Keywords: Stochastic volatility, activity index, Blumenthal-Getoor index, jumps, VIX index, jump risk premium
Testing for jumps in conditionally Gaussian ARMA-GARCH models, a robust approach, Sébastien Laurent, Christelle Lecourt and Franz Palm,
from HAL
(2016)
Keywords: forecasting, GARCH, Jumps, test
Testing for jumps in conditionally Gaussian ARMA–GARCH models, a robust approach, Sébastien Laurent, Christelle Lecourt and Franz Palm,
in Computational Statistics & Data Analysis
(2016)
Keywords: Jumps; GARCH; Test; Forecasting;
Chasing Volatility. A Persistent Multiplicative Error Model With Jumps, Massimiliano Caporin, Eduardo Rossi and Paolo Santucci De Magistris,
from Dipartimento di Scienze Economiche "Marco Fanno"
(2014)
Keywords: Multiplicative Error Model with Jumps, Jumps in volatility, Realized measures, Volatility-at-Risk.
Chasing volatility - A persistent multiplicative error model with jumps, Massimiliano Caporin, Eduardo Rossi and Paolo Santucci de Magistris,
from Department of Economics and Business Economics, Aarhus University
(2014)
Keywords: Multiplicative Error Model with Jumps, Jumps in volatility, Realized measures, Volatility-at-Risk
Asymptotic Inference for Common Factor Models in the Presence of Jumps, Yohei Yamamoto and 庸平 山本,
from Hitotsubashi Institute for Advanced Study, Hitotsubashi University
(2016)
Keywords: outliers, large-dimensional factor models, principal components, jumps, common jumps
Detection of jumps by wavelets in a heteroscedastic autoregressive model, Heung Wong, Waicheung Ip and Yuan Li,
in Statistics & Probability Letters
(2001)
Keywords: Heteroscedasticity Autoregressive model Jumps Wavelets
Jumps in Oil Prices: The Role of Economic News, John Elder, Hong Miao and Sanjay Ramchander,
in The Energy Journal
(2013)
Keywords: Oil; Jumps; Macroeconomic news announcements
Currency jumps, cojumps and the role of macro news, Arjun Chatrath, Hong Miao, Sanjay Ramchander and Sriram Villupuram,
in Journal of International Money and Finance
(2014)
Keywords: Currency jumps; Cojumps; Macroeconomic news;
Press Freedom and Jumps in Stock Prices, Thorsten Lehnert,
from International Institute of Social and Economic Sciences
(2014)
Keywords: Press Freedom, Asset Pricing, Jumps, Volatility, Skewness
Jumps in the convenience yield of crude oil, Charles Mason and Neil Wilmot,
in Resource and Energy Economics
(2020)
Keywords: Crude oil; Convenience yield; Jumps; GARCH;
Jumps into democracy: The transition in the Polity Index, Martin Paldam and Erich Gundlach,
from Department of Economics and Business Economics, Aarhus University
(2016)
Keywords: Transition path, triggering events, regime jumps
Conditional jumps in volatility and their economic determinants, Massimiliano Caporin, Eduardo Rossi and Paolo Santucci de Magistris,
from Dipartimento di Scienze Economiche "Marco Fanno"
(2011)
Keywords: Volatility, Jumps in volatility, Realized range, HAR.
The Effect of Macro News on Volatility and Jumps, Dimitrios Vortelinos,
in Annals of Economics and Finance
(2015)
Keywords: Macroeconomic announcements, Volatility, Jumps, Financial markets
Trading activity, realized volatility and jumps, Pierre Giot, Sébastien Laurent and Mikael Petitjean,
in Journal of Empirical Finance
(2010)
Keywords: Volume Volatility Transactions Jumps Bi-power variation
What triggers stock market jumps?, Scott Baker, Nicholas Bloom, Steven Davis and Marco Sammon,
from Centre for Economic Performance, LSE
(2021)
Keywords: Stock markets, upward and downward jumps, newspapers
Preferences, Levy Jumps and Option Pricing, Chenghu Ma,
from Wang Yanan Institute for Studies in Economics (WISE), Xiamen University
(2013)
Keywords: equilibrium option pricing, recursive utility, Levy jumps.
Volatility jumps: The role of geopolitical risks, Konstantinos Gkillas (Gillas), Rangan Gupta and Mark Wohar,
in Finance Research Letters
(2018)
Keywords: Stock market volatility jumps; Geopolitical risks;
What triggers stock market jumps?, Scott Baker, Nicholas Bloom, Steven Davis and Marco Sammon,
from Centre for Economic Performance, LSE
(2021)
Keywords: Stock markets, upward and downward jumps, newspapers
Volatility Jumps: The Role of Geopolitical Risks, Konstantinos Gkillas (Gillas), Rangan Gupta and Mark Wohar,
from University of Pretoria, Department of Economics
(2018)
Keywords: Stock Market Volatility Jumps, Geopolitical Risks
Fixed jumps of additive processes, Ming Liao,
in Statistics & Probability Letters
(2013)
Keywords: Additive processes; Fixed jumps; Independent increments; Lévy–Itô representation;
Regime Jumps in Electricity Prices, Ronald Huisman and Ronald Mahieu,
from Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam
(2001)
Keywords: electricity prices, international energy markets, jumps, mean reversion, stochastic models
Systemic co-jumps, Massimiliano Caporin, Aleksey Kolokolov and Roberto Renò,
in Journal of Financial Economics
(2017)
Keywords: Jumps; Return predictability; Systemic events; Variance risk premium;
Systemic co-jumps, Massimiliano Caporin, Alexey Kolokolov and Roberto Renò,
from Leibniz Institute for Financial Research SAFE
(2016)
Keywords: Jumps, Return predictability, Systemic events, Variance Risk Premium
Volatility jumps and their economic determinants, Massimiliano Caporin, Eduardo Rossi and Paolo Santucci de Magistris,
from Department of Economics and Business Economics, Aarhus University
(2014)
Keywords: Volatility jumps, Realized range, HAR-V-J, CDS
Volatility Jumps and Their Economic Determinants, Massimiliano Caporin, Eduardo Rossi and Paolo Santucci de Magistris,
in Journal of Financial Econometrics
(2016)
Keywords: CDS, HAR-V-J, realized range, volatility jumps
Optimal stopping for a diffusion with jumps, Ernesto Mordecki,
in Finance and Stochastics
(1999)
Keywords: Diffusion with jumps, optimal stopping, American options, derivative pricing
Effects of idiosyncratic jumps and co-jumps on oil, gold, and copper markets, Artur Semeyutin, Giray Gözgör, Chi Keung Lau and Bing Xu,
in Energy Economics
(2021)
Keywords: Oil market; Gold market; Copper market; Portfolio allocations; Jumps and Co-jumps; COVID-19 pandemic;
Testing for Co-jumps in Financial Markets, Jan Novotný and Giovanni Urga,
in Journal of Financial Econometrics
(2018)
Keywords: co-features, Dow Jones Industrial Average 30 index, jumps and co-jumps, portfolio diversification
Jumps in Energy and Non-Energy Commodities, Elie Bouri and Rangan Gupta,
from University of Pretoria, Department of Economics
(2020)
Keywords: Realized volatility, energy and non-energy commodities, jumps, co-jumps, macroeconomic news
The Impact of Stock Market Jumps on Time-Varying Return Correlations: Empirical Evidence from the Baltic Countries, Jörgen Hellström and Albina Soultanaeva,
from Umeå University, Department of Economics
(2010)
Keywords: Correlated jumps; contagion
Volatility estimation for cryptocurrencies: Further evidence with jumps and structural breaks, Amélie Charles and Olivier Darné,
in Economics Bulletin
(2019)
Keywords: Cryptocurrency, GARCH, volatility, jumps, breaks.
Analysis of stochastic two-prey one-predator model with Lévy jumps, Meng Liu, Chuanzhi Bai, Meiling Deng and Bo Du,
in Physica A: Statistical Mechanics and its Applications
(2016)
Keywords: Random noise; Lévy jumps; Stability;
Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility, Andrew Patton and Kevin Sheppard,
in The Review of Economics and Statistics
(2015)
Keywords: volatility, trade, market, signed jumps
Identifying the Brownian Covariation from the Co-Jumps Given Discrete Observations, Cecilia Mancini and Fabio Gobbi,
from Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa
(2010)
Keywords: co-jumps, integrated covariation, integrated variance, finite activity jumps, infinite activity jumps, threshold estimator
When do jumps matter for portfolio optimization?, Marius Ascheberg, Nicole Branger and Holger Kraft,
from Leibniz Institute for Financial Research SAFE
(2013)
Keywords: Optimal investment, jumps, stochastic volatility, welfare loss
Stock market volatility and jumps in times of uncertainty, Anastasios Megaritis, Nikolaos Vlastakis and Athanasios Triantafyllou,
from University of Essex, Essex Business School
(2020)
Keywords: Jumps, Bipower variation, Realized volatility, Macroeconomic Uncertainty
Stability of a stochastic delay commensalism model with Lévy jumps, Meiling Deng,
in Physica A: Statistical Mechanics and its Applications
(2019)
Keywords: Commensalism system; Lévy jumps; Time delay; Stability;
Stock market volatility and jumps in times of uncertainty, Anastasios Megaritis, Nikolaos Vlastakis and Athanasios Triantafyllou,
in Journal of International Money and Finance
(2021)
Keywords: Jumps; Bipower variation; Realized volatility; Macroeconomic Uncertainty;
How Jumps Affect Liquidity? The Evidence from Poland, Barbara Będowska-Sójka,
in Czech Journal of Economics and Finance (Finance a uver)
(2017)
Keywords: liquidity, jumps, intraday data, event study
Jumps in equilibrium prices and market microstructure noise, Suzanne S. Lee and Per A. Mykland,
in Journal of Econometrics
(2012)
Keywords: Jumps; Noise; Nonparametric tests; High frequency data;
Lp estimates for fully coupled FBSDEs with jumps, Juan Li and Qingmeng Wei,
in Stochastic Processes and their Applications
(2014)
Keywords: Fully coupled FBSDEs with jumps; Lp estimates;
The Role of Jumps in Realized Volatility Modeling and Forecasting, Massimiliano Caporin,
in Journal of Financial Econometrics
(2023)
Keywords: forecasting, jumps, liquidity, realized volatility, staleness
Incomplete financial markets and jumps in asset prices, Hervé Crès, Tobias Markeprand and Mich Tvede,
in Economic Theory
(2016)
Keywords: Financial markets, General equilibrium, Jumps in asset prices
Incomplete Financial Markets and Jumps in Asset Prices, Hervé Crès, Tobias Markeprand and Mich Tvede,
from University of Copenhagen. Department of Economics
(2009)
Keywords: general equilibrium; financial markets; jumps in asset prices
Realized volatility transmission: The role of jumps and leverage effects, Michael Soucek and Neda Todorova,
in Economics Letters
(2014)
Keywords: Volatility transmission; Jumps; Leverage effects; Realized volatility;
Jumps in Geopolitical Risk and the Cryptocurrency Market: The Singularity of Bitcoin, Elie Bouri, Rangan Gupta and Xuan Vo,
from University of Pretoria, Department of Economics
(2020)
Keywords: Geopolitical risk, Bitcoin, Cryptocurrencies, Jumps, GARCH
Forecasting the oil futures price volatility: Large jumps and small jumps, Jing Liu, Feng Ma, Ke Yang and Yaojie Zhang,
in Energy Economics
(2018)
Keywords: Volatility forecasting; oil futures price; Large and small jumps; Predictive evaluation;
Do Jumps Matter? Forecasting Multivariate Realized Volatility allowing for Common Jumps, Yin Liao, Heather Anderson and Farshid Vahid,
from Monash University, Department of Econometrics and Business Statistics
(2010)
Keywords: Realized Volatility, Bipower Variation, Jumps, Common Factors, Forecasting
Smoothness of harmonic functions for processes with jumps, Jean Picard and Catherine Savona,
in Stochastic Processes and their Applications
(2000)
Keywords: Harmonic functions Diffusions with jumps Excessive measures Malliavin calculus
On stochastic ordering for diffusion with jumps and applications, Xinsheng Zhang,
in Statistics & Probability Letters
(2007)
Keywords: Invariant probability measure Comparison theorem Diffusion processes with jumps
Press freedom and jumps in stock prices, Sara Abed Masrorkhah and Thorsten Lehnert,
in Economic Systems
(2017)
Keywords: Press freedom; News; Governance; Welfare; Jumps; Stock markets;
The effect of short selling on volatility and jumps, Glenn Kit Foong Ho, Sirimon Treepongkaruna, Marvin Wee and Chaiyuth Padungsaksawasdi,
in Australian Journal of Management
(2022)
Keywords: Jumps; order imbalance; realized volatility; short selling; trading volume
Volatility jumps and their determinants in REIT returns, Babatunde O. Odusami,
in Journal of Economics and Business
(2021)
Keywords: REITs; Real Estate; Jumps; Bipower Variation; Autoregressive Conditional Hazard;
Volatility forecasting: the jumps do matter, Fulvio Corsi, Davide Pirino and Roberto Renò,
from Department of Economics, University of Siena
(2008)
Keywords: volatility forecasting, jumps, bipower variation, threshold estimation, stock, bond
Risk Appetite and Jumps in Realized Correlation, Riza Demirer, Konstantinos Gkillas, Christos Kountzakis and Amaryllis Mavragani,
in Mathematics
(2020)
Keywords: realized correlation jumps; stock-bond correlation; time-varying risk aversion
Identification of jumps in financial price series, Jörgen Hellström and Carl Lönnbark,
from Umeå University, Department of Economics
(2011)
Keywords: Financial econometrics; jumps; realized variance; bipower variation; stock price
Deep Learning, Jumps, and Volatility Bursts, Oksana Bashchenko and Alexis Marchal,
from Swiss Finance Institute
(2020)
Keywords: Jumps, Volatility Burst, High-Frequency Data, Deep Learning, LSTM
The impact of co-jumps in the oil sector, Márcio Laurini, Roberto Mauad and Fernando Antônio Lucena Aiube,
in Research in International Business and Finance
(2020)
Keywords: Oil prices; Jumps; Stochastic volatility (SV); Risk management;
OPEC news and jumps in the oil market, Konstantinos Gkillas, Rangan Gupta, Christian Pierdzioch and Seong-Min Yoon,
in Energy Economics
(2021)
Keywords: Oil market jumps; OPEC announcements; Nonparametric quantile causality;
What triggers stock market jumps?, Scott Baker, Nicholas Bloom, Steven Davis and Marco C. Sammo,
from London School of Economics and Political Science, LSE Library
(2021)
Keywords: stock markets; upward and downward jumps; newspapers; SES 20180940
Volatility Forecasting: The Jumps Do Matter, Fulvio Corsi, Davide Pirino and Roberto Renò,
from Institute of Economic Research, Hitotsubashi University
(2009)
Keywords: volatility forecasting, jumps, bipower variation, threshold estimation, stock, bond
OPEC News and Jumps in the Oil Market, Konstantinos Gkillas, Rangan Gupta, Christian Pierdzioch and Seong-Min Yoon,
from University of Pretoria, Department of Economics
(2020)
Keywords: Oil market jumps, OPEC announcements, Nonparametric quantile causality
Asian options with jumps, Ching-Sung Chou and Hsien-Jen Lin,
in Statistics & Probability Letters
(2006)
Keywords: Asian options with jumps Incomplete financial market Resolvent Markov processes Cadlag processes
Tests for Jumps in Yield Spreads, Lars Winkelmann and Wenying Yao,
from Berlin School of Economics
(2023)
Keywords: High-frequency data, jumps, sequential testing, intersection union test, term spread, break-even inflation
Testing for self-excitation in jumps, H. Peter Boswijk, Roger Laeven and Xiye Yang,
in Journal of Econometrics
(2018)
Keywords: Self-excitation; Jumps; Semimartingale; Spot jump intensity; Discrete sampling; High frequency data; Financial crisis;
The identification of price jumps, Jan Hanousek, Evžen Kočenda and Novotný Jan,
in Monte Carlo Methods and Applications
(2012)
Keywords: Price jumps, price-jump indicators, non-parametric testing, Monte Carlo simulations, financial econometrics
The Identification of Price Jumps, Jan Hanousek, Evžen Kočenda and Jan Novotny,
from The Center for Economic Research and Graduate Education - Economics Institute, Prague
(2011)
Keywords: price jumps; price-jump indicators; non-parametric testing; Monte Carlo simulations; financial econometrics
Blockchain and crypto-exposed US companies and major cryptocurrencies: The role of jumps and co-jumps, Fang Xu, Elie Bouri and Oguzhan Cepni,
in Finance Research Letters
(2022)
Keywords: Block chain and crypto-exposed companies; Cryptocurrencies; Jumps and co-jumps; GARCH-based model; COVID-19 outbreak;
Pareto efficiency of infinite-horizon cooperative stochastic differential games with Markov jumps and Poisson jumps, Po Hu, Hongbin Ma, Xiaoguang Yang and Yifen Mu,
in Mathematics and Computers in Simulation (MATCOM)
(2024)
Keywords: Stochastic differential games; Poisson jumps; Markov jumps; Pareto efficiency; Cooperative games;
Uncertainty and realized jumps in the pound-dollar exchange rate: evidence from over one century of data, Gkillas Konstantinos, Rangan Gupta and Vortelinos Dimitrios I.,
in Studies in Nonlinear Dynamics & Econometrics
(2023)
Keywords: exchange rates, realized jumps, uncertainty
Uncertainty and Volatility Jumps in the Pound-Dollar Exchange Rate: Evidence from Over One Century of Data, Konstantinos Gkillas (Gillas), Rangan Gupta and Dimitrios Vortelinos,
from University of Pretoria, Department of Economics
(2018)
Keywords: Exchange Rates, Volatility Jumps, Uncertainty
A note on the valuation of CDS options and extension risk in a structural model with jumps, Amelie Hüttner and Matthias Scherer,
in International Journal of Financial Engineering (IJFE)
(2016)
Keywords: CDS options, extension risk, structural model with jumps
Forecasting crude-oil market volatility: Further evidence with jumps, Amélie Charles and Olivier Darné,
from HAL
(2017)
Keywords: Crude oil returns,Volatility forecasting,Jumps
Dynamics of a stochastic one-prey two-predator model with Lévy jumps, Meng Liu and Chuanzhi Bai,
in Applied Mathematics and Computation
(2016)
Keywords: White noises; Lévy jumps; Persistence; Extinction; Stability;
Forecasting crude-oil market volatility: Further evidence with jumps, Amélie Charles and Olivier Darné,
in Energy Economics
(2017)
Keywords: Crude oil returns; Volatility forecasting; Jumps;
Dynamics of a stochastic population model with Allee effect and Lévy jumps, Meiling Deng,
in Physica A: Statistical Mechanics and its Applications
(2019)
Keywords: Allee effect; Lévy jumps; Extinction; Stochastic permanence;
Can risk-neutral skewness and kurtosis subsume the information content of historical jumps?, Ging-Ginq Pan, Yung-Ming Shiu and Tu-Cheng Wu,
in Journal of Financial Markets
(2022)
Keywords: Volatility forecasting; Risk-neutral moments; Jumps;
Biomechanics of Rotational Movement in Off-Ice Figure Skating Jumps: Applications to Training, Mazurkiewicz Anna,
in Polish Journal of Sport and Tourism
(2021)
Keywords: figure skating, biomechanics, rotation, training, jumps, forces
Linear-quadratic term structure models - Toward the understanding of jumps in interest rates, George Jiang and Shu Yan,
in Journal of Banking & Finance
(2009)
Keywords: Interest rates Term structure Jumps Bonds
The Maximum Principle for Stochastic Control Problem with Jumps in Progressive Structure, Yuanzhuo Song and Zhen Wu,
in Journal of Optimization Theory and Applications
(2023)
Keywords: Progressive structure, Random jumps, The maximum principle
Price Jumps in Visegrad Country Stock Markets: An Empirical Analysis, Jan Novotny,
from The Center for Economic Research and Graduate Education - Economics Institute, Prague
(2010)
Keywords: financial markets; Visegrad region; price jumps.
Monetary Policy Uncertainty and Volatility Jumps in Advanced Equity Markets, Elie Bouri, Konstantinos Gkillas (Gillas), Rangan Gupta and Clement Kyei,
from University of Pretoria, Department of Economics
(2019)
Keywords: Stock Market Volatility Jumps, Monetary Policy Uncertainty
The explanatory power of signed jumps for the risk-return tradeoff, Benoît Sévi and César Baena,
from HAL
(2013)
Keywords: ICAPM, Realized volatility, risk-return tradeoff, signed jumps.
Outliers and Time-Varying Jumps in the Cryptocurrency Markets, Anupam Dutta and Elie Bouri,
in JRFM
(2022)
Keywords: Bitcoin; cryptocurrencies; outliers; GARCH-jump; time-varying jumps
Identi�cation of jumps in �financial price series, Jörgen Hellström and Carl Lönnbark,
from University Library of Munich, Germany
(2011)
Keywords: Financial econometrics, jumps, realized variance, bipower variation, stock price
Econometrics of co-jumps in high-frequency data with noise, Markus Bibinger and Lars Winkelmann,
in Journal of Econometrics
(2015)
Keywords: Co-jumps; Covolatility estimation; Microstructure noise; Non-synchronous observations; Truncation;
Threshold of a stochastic SIR epidemic model with Lévy jumps, Yanli Zhou and Weiguo Zhang,
in Physica A: Statistical Mechanics and its Applications
(2016)
Keywords: Ito formula; Lévy jumps; Threshold; Persistence in mean; Extinction;
Dynamics of an imprecise SIRS model with Lévy jumps, Kangbo Bao, Qimin Zhang, Libin Rong and Xining Li,
in Physica A: Statistical Mechanics and its Applications
(2019)
Keywords: Stochastic SIRS epidemic model; Lévy jumps; Interval number; Extinction; Persistence;
On solutions of backward stochastic differential equations with jumps and applications, Situ Rong,
in Stochastic Processes and their Applications
(1997)
Keywords: BSDE with jumps Adapted solution PDIE Ito formula Convergence theorem
Simulation of BSDEs with jumps by Wiener Chaos expansion, Christel Geiss and Céline Labart,
in Stochastic Processes and their Applications
(2016)
Keywords: Backward stochastic differential equations with jumps; Wiener Chaos expansion; Numerical method;
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