Geodesic
Minimizing the variance of estimate of mathematical expectation of a~diffusion process functional by parametric transformation of the parabolic boundary value problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 2, pp. 141-153

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This paper is associated with finding the ways of reducing the variance of the estimate of mathematical expectation of the functional of a diffusion process moving in a domain with an absorbing boundary. The estimate of mathematical expectation of the functional is obtained using a numerical solution of stochastic differential equations (SDE's) by the Euler method. A formula of the limiting variance at decreasing the integration step in the Euler method is obtained. A method of reducing the variance value of the estimate based on transformation of the parabolic boundary value problem corresponding to the diffusion process is proposed. Some numerical results are presented. 
@article{SJVM_2011_14_2_a2,
     author = {S. A. Gusev},
     title = {Minimizing the variance of estimate of mathematical expectation of a~diffusion process functional by parametric transformation of the parabolic boundary value problem},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {141--153},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2011_14_2_a2/}
}
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S. A. Gusev. Minimizing the variance of estimate of mathematical expectation of a~diffusion process functional by parametric transformation of the parabolic boundary value problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 2, pp. 141-153. http://geodesic.mathdoc.fr/item/SJVM_2011_14_2_a2/