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. 
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     title = {Minimizing the variance of estimate of mathematical expectation of a~diffusion process functional by parametric transformation of the parabolic boundary value problem},
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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/

[1] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[2] Uryasev S. P., Adaptivnye algoritmy stokhasticheskoi optimizatsii i teorii igr, Nauka, M., 1990 | MR

[3] Gusev S. A., “Otsenka proizvodnykh po parametram funktsionalov diffuzionnogo protsessa, dvizhuschegosya v oblasti s pogloschayuschei granitsei”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 11:4 (2008), 385–404 | Zbl

[4] Gobet E., Menozzi S., “Stopped diffusion process: boundary corrections and overshoot”, Stochastic Process. Appl., 120 (2010), 130–162 | DOI | MR | Zbl

[5] Gikhman I. I., Skorokhod A. V., Stokhasticheskie differentsialnye uravneniya, Naukova dumka, Kiev, 1968 | MR | Zbl