ON APPROXIMATE EVALUATION OF MATHEMATICAL EXPECTATION OF FUNCTIONALS FROM THE SOLUTION TO THE LINEAR ÎTO–LÉVY EQUATION
Abstract
Functional quadrature formulas for evaluation of mathematical expectation of nonlinear functionals from the solution to the linear Îto–Lévy equation are constructed. The formulas are exact for third-degree functional polynomials from the solution. The error of the constructed composed formula is obtained for a class of integral-form functionals.
References
1. Øksendal B., Sulem A. Applied Stochastic Control of Jump Diffusions. Berlin: Springer, 2009.
2. Kloeden P. E., Platen E. Numerical Solution of Stochastic Differential Equations. Berlin: Springer, 1999.
3. Egorov A. D., Sobolevsky P. I., Yanovich L. A. Functiona Integrals. Approximate Evaluation and Applications. Kluwer Academic Publishers, 1993.
4. Egorov A. D., Zherelo A. // Monte Carlo Methods and Applications. 2010. Vol. 10, N 3–4. P. 257–264.
5. Egorov A. D., Sabelfeld K. K. // Monte Carlo Methods and Applications. 2010. Vol. 16, N 2. P. 95–127.
6. Zherelo A. V. // Monte Carlo Methods and Applications. 2013. Vol. 19, N 4. P. 183–200.
7. Егоров А. Д., Уласик А. Ф. // Весцi НАН Беларусi. Сер. фiз.-мат. навук. 2012. № 3. С. 78–82.
8. Егоров А. Д. // Весцi НАН Беларусi. Сер. фiз.-мат. навук. 2013. № 1. С. 8–12.
9. Егоров А. Д. // Тр. Ин-та математики. 2014. Т. 22, № 1. С. 70–77.
10. Малютин В. Б. // Тр. Ин-та математики. 2014. Т. 22, № 1. С. 107–114.
11. Гихман И. И., Скороход А. В. Стохастические дифференциальные уравнения. Киев: Наукова думка, 1968.
Review
Views: 833
Email this article 