APPROXIMATE FORMULAS FOR CALCULATING THE MATHEMATICAL EXPECTATION OF FUNCTIONALS OF SOLUTION OF THE ITO EQUATIONS IN A HILBERT SPACE
Abstract
About the Author
A. D. EgorovBelarus
D. Sc. (Physics and Mathematics), Professor, Chief researcher
References
1. Daletskii Yu. L. Measures and differential equations in infinite spaces. Moscow, Nauka, 1983. 383 p. (in Russian)
2. Da Prato G., Zabczyk J. Stochastic Equations in Infinite Dimensions. Cambridge University Press, 1992. 454 p.
3. Gawarecki G., Mandrekar V. Stochastic Differential Equations in Infinite Dimensions with Applications to Stochastic Partial Differential Equations. Springer, 2011. 274 p. doi: 10.1007/978-3-642-16194-0.
4. Dalang R. C., Khoshnevisan D., Mueller C., Nualart D., Xiao Y. A Minicourse on Stochastic Partial Differential Equations. Springer, 2006. 222 p.
5. Hairer M. An Introduction to Stochastic PDEs. The University of Warwick, Courant Institute, 2009. 78 p.
6. Jentzen A., Kloeden P. E. Taylor Approximations for Stochastic Partial Differential Equations. Philadelphia, SIAM Press, 2011. 235 p.
7. Edvards R. Functional analysis. Theory and applications. Moscow, Mir, 1969. 1071 p. (in Russian)
8. Egorov A. D., Sobolevsky P. I., Yanovich L. A. Functional integrals: Approximate evaluations and applications. Kluwer Academic Publishers, 1993. 418 p.
9. Egorov A. D., Zhidkov E. P., Lobanov Yu. Yu. An introduction to the theory and applications of functional integration. Мoscow, Fizmatlit Publ., 2006. 400 p. (in Russian)
10. Egorov A., Sabelfeld K. Approximate formulas for expectations of functionals of solutions to stochastic differential equations. Monte Carlo methods and applications, 2010, vol. 16, no. 2, pp. 95–127. doi: 10.1515/mcma.2010.003.