This article is cited in 3 scientific papers (total in 3 papers)
Minimizing the variance of estimate of mathematical expectation of a diffusion process functional by parametric transformation of the parabolic boundary value problem
Abstract:
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.
Key words:
diffusion process, stochastic differential equations, absorbing boundary, variance of an estimate of the functional, Euler method.
Citation:
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”, Sib. Zh. Vychisl. Mat., 14:2 (2011), 141–153; Num. Anal. Appl., 4:2 (2011), 114–124
\Bibitem{Gus11}
\by S.~A.~Gusev
\paper Minimizing the variance of estimate of mathematical expectation of a~diffusion process functional by parametric transformation of the parabolic boundary value problem
\jour Sib. Zh. Vychisl. Mat.
\yr 2011
\vol 14
\issue 2
\pages 141--153
\mathnet{http://mi.mathnet.ru/sjvm432}
\transl
\jour Num. Anal. Appl.
\yr 2011
\vol 4
\issue 2
\pages 114--124
\crossref{https://doi.org/10.1134/S1995423911020030}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79957857193}
Linking options:
https://www.mathnet.ru/eng/sjvm432
https://www.mathnet.ru/eng/sjvm/v14/i2/p141
This publication is cited in the following 3 articles:
S. A. Gusev, “O dispersii otsenki funktsionala ot diffuzionnogo protsessa v oblasti s otrazhayuschei granitsei”, Sib. zhurn. vychisl. matem., 25:4 (2022), 359–369
S. A. Gusev, “On the Variance of Estimation of a Diffusion Process Functional in a Domain with a Reflecting Boundary”, Numer. Analys. Appl., 15:4 (2022), 293
T. A. Averina, K. A. Rybakov, “A modification of numerical methods for stochastic differential equations with the first integral”, Num. Anal. Appl., 12:3 (2019), 203–218
Citation in format AMSBIB
Contact us: