ORDER OF CONVERGENCE OF APPROXIMATIONS FOR ONE CLASS OF FUNCTIONALS OF THE WIENER PROCESS
Abstract
The result on the order of convergence of the approximate formula is obtained for evaluation of the mathematical expectation of one class of special-type functionals of the Wiener process. The formula is based on the use of sampling the time interval and the quadrature formulas exact for third-degree functional polynomials.
About the Author
A. D. Egorov
Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
Belarus
Belarus
References
1. Zherelo, A. V. On convergence of the method based on approximately exact formulas for functional polynomials for calculations of expectation of the functionals to solution of stochastic differential equations / A. V. Zherelo // Monte Carlo Methods and Applications. – 2013. – Vol. 19 (4). – P. 183–200.
2. Egorov, A. D. Functional integrals: Approximate evaluations and applications / A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich. – [S. l.]: Kluwer Academic Publishers, 1993.
3. Егоров, А. Д. Введение в теорию и приложения функционального интегрирования / А. Д. Егоров, Е. П. Жидков, Ю. Ю. Лобанов. – М.: Физматлит, 2006.
4. Egorov, A. D. Approximate formulas for expectations of functionals of solutions to stochastic differential equations / A. D. Egorov, K. K. Sabelfeld // Monte Carlo Methods and Applications. – 2010. – Vol. 16, N 2. – Р. 95–127.
Review
Views: 587
Email this article 