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Sequential control variates for functionals of Markov processes. (English) Zbl 1093.65003

Summary: 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.

MSC:

65C50 Other computational problems in probability (MSC2010)
65C05 Monte Carlo methods
60J60 Diffusion processes
60J25 Continuous-time Markov processes on general state spaces
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