APPROXIMATE FORMULAS FOR EVALUATION OF ONE-CLASS FUNCTIONALS OF THE POISSON PROCESS
Abstract
This work is devoted to the construction of approximate formulas for calculation of mathematical expectation of nonlinear functionals defined along the trajectories of random processes. Computation of mathematical expectation of functionals of random processes by the quadrature method is the task that depends heavily on a form in which the process is given. A lot of functional quadrature formulas are built in the cases where the characteristic functional of the process is known in explicit form. Some results are obtained in the cases where the process is the solution of the stochastic differential Itό equation. Recently, the author has proposed the approach to an approximate evaluation of mathematical expectation of a class of nonlinear random functionals based on the use of the Wiener chaos expansion. The article uses chaos expansion with respect to multiple Poisson – Ito integrals to construct functional quadrature formulas for calculating nonlinear functionals of the stochastic process defined on the probability space generated by the Poisson process. The formula is exact for the thirddegree symmetric functional polynomial, so the product formula of multiple Poisson – Ito integrals is used for construction.
About the Author
A. D. Egorov
Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
Belarus
D. Sc. (Physics and Mathematics), Chief Researcher
Belarus
D. Sc. (Physics and Mathematics), Chief Researcher
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