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Journal Articles SIAM Journal on Numerical Analysis Year : 2006

Sequential control variates for functionals of Markov processes

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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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Dates and versions

hal-01479838 , version 1 (28-02-2017)

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Emmanuel Gobet, Sylvain Maire. Sequential control variates for functionals of Markov processes. SIAM Journal on Numerical Analysis, 2006, 43 (3), pp.1256-1275. ⟨10.1137/040609124⟩. ⟨hal-01479838⟩
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