Article2005

Sequential Control Variates for Functionals of Markov Processes

32 citations0/0 files storedSIAM Journal on Numerical Analysis

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Stochastic processes and financial applications Markov Chains and Monte Carlo Methods Mathematical Approximation and Integration

Abstract

Using a sequential control variates algorithm, we compute Monte Carlo approximations of solutions of linear partial differential equations connected to linear Markov processes by the Feynman--Kac formula. It includes diffusion processes with or without absorbing/reflecting boundary and jump processes. We prove that the bias and the variance decrease geometrically with the number of steps of our algorithm. Numerical examples show the efficiency of the method on elliptic and parabolic problems.

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1999Continuous Martingales and Brownian Motion 2008Stochastic differential equations and applications 1976Stochastic Differential Equations and Applications 2000Weak approximation of killed diffusion using Euler schemes 1995Efficient Monte Carlo Simulation of Security Prices 1993Continuous martingales and brownian motion 1994Variance Reduction for Simulated Diffusions 2001Euler schemes and half-space approximation for the simulation of diffusion in a domain

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