stochastic differential equations, Monte Carlo method, diffusion processes, parametric derivatives, Malliavin calculus.
UDC:
519.676
Subject:
Numerical methods for sensitivity analysis of stochastic differential equations.
Estimation of derivatives with respect to parameters of a functional of a diffusion process moving in the given domain.
Main publications:
S. A. Gusev, Estimation of the coefficients in the parabolic equation by the statistical simulation of diffusion trajectories // Russian Journal of Numerical Analysis and Mathematical Modelling. VSP Publisher, Netherlands. 2003, Vol. 18, No 4, pp. 297–306.
S. A. Gusev, Monte Carlo estimates of the solution of a parabolic equation and its derivatives made by solving stochastic differential equations, Communications in Nonlinear Science and Numerical Simulation, Elsevier Science, Amsterdam, Vol. 9, Issue 2, 2003, pp. 177–185.
S. A. Gusev, Using SDE for solving inverse parabolic boundary value problem with a Neumann boundary condition // Russian Journal of Numerical Analysis and Mathematical Modelling. Vol. 22, No 5, pp. 449–470 (2007).
S. A. Gusev, V. N. Nikolaev, “On the influence of random environmental factors on heat
transfer processes in aircrafts”, Sib. Zh. Vychisl. Mat., 27:2 (2024), 165–172
2022
2.
S. A. Gusev, “On the variance of the estimate of the functional of the diffusion process in a domain with a reflecting boundary”, Sib. Zh. Vychisl. Mat., 25:4 (2022), 359–369
2015
3.
S. A. Gusev, “Application of SDE's to estimating the solution of heat equations with discontinuous coefficients”, Sib. Zh. Vychisl. Mat., 18:2 (2015), 147–161; Num. Anal. Appl., 8:2 (2015), 122–134
S. A. Gusev, N. G. Dokuchaev, “On differentiation of functionals containing the first exit of a diffusion process from a domain”, Teor. Veroyatnost. i Primenen., 59:1 (2014), 159–168; Theory Probab. Appl., 59:1 (2015), 136–144
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
S. A. Gusev, “Estimation of derivatives with respect to parameters of a functional of a diffusion process moving in a domain with absorbing boundary”, Sib. Zh. Vychisl. Mat., 11:4 (2008), 385–404; Num. Anal. Appl., 1:4 (2008), 314–331
S. A. Gusev, “Solving SDE's numerically to estimate parametric derivatives of the solution to a parabolic boundary value problem with a Neumann boundary condition”, Sib. Zh. Vychisl. Mat., 10:3 (2007), 237–246
S. A. Gusev, “Monte Carlo estimates of derivatives with respect to parameters of the solution of the parabolic equation based on numerical SDE solution”, Sib. Zh. Vychisl. Mat., 8:4 (2005), 297–306
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