Nonlinear Phenomena in Complex Systems, 2025, Vol.28, No.2, pp.137

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2025, Vol.28, No.2, pp.137 - 143

On an Approximate Formula for Functionals with Respect to a Solution of Stochastic Differential Equation with a Drift and Random Process with Jumps

A. Zherelo

Formula for approximate calculation of mathematical expectations of functionals on solutions of a stochastic differential equation with a drift and with a random process with jumps has been constructed. The random part with jumps is specified by a stochastic integral over a stochastic Poisson process. The stochastic integral used is a generalization of the Ito integral to the case of a martingale with discontinuities. Examples of the formula usage to calculate mathematical expectations are given.

Key words: stochastic processes with discontinuities, moments of a random process, approximate formula, weak approximation methods

DOI: https://doi.org/10.5281/zenodo.15081335

Full text: Acrobat PDF (377 KB) Open Access