Invariant surfaces for certain classes of systems of the second-order to stochastic differential equations with jumps

Authors

DOI:

https://doi.org/10.17721/1812-5409.2022/3.2

Keywords:

stochastic differential equations with jumps, invariant surfaces

Abstract

In this paper, we consider the concept of invariant sets of inhomogeneous stochastic differential equations with jumps. For certain classes of systems of the second order of inhomogeneous stochastic differential equations with jumps the necessary and sufficient conditions for the invariance of the corresponding surfaces are established. The obtained results provide opportunities to find the invariant surfaces and conditions of their invariance for the specified classes of stochastic differential equations.

Pages of the article in the issue: 22 - 27

Language of the article: Ukrainian

References

KULINICH, G. L., BABCHUK V.G. (1976) Invariant sets of system of linear stochastic Ito differential equations of the second order // Visn. Ky¨ıv. Univ. , No. 18, P. 136–139.

KULINICH, G. L., KUSHNIRENKO, S. V. (2000) Invariant sets for systems of stochastic differential equations without aftereffect // Theory Probab. Math. Stat., 63, P. 112–118.

Handbook on Probability and Mathematical statistics // V.S. Korolyuk, N.I. Portenko, A.V. Skorokhod, A.F. Turbin / Ed. V.S. Korolyuk. – M.: Nauka, 1985. – 640 p.

KULINICH, G. L., KUSHNIRENKO, S. V. (2005) Invariant sets of systems of stochastic differential equations with jumps // Nonlinear Oscillations, 8, No. 2, P. 234–240.

KULINICH, G. L. (1998) On invariant sets of the system of the second order of stochastic differential equations without aftereffect // Theses of the International science conf. “Development and application of mathematical methods in scientific and technical research”, October 8–10, 1998, Lviv. Bulletin “Applied mathematics”. No. 337, V. 1.

– P. 126–127.

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Published

2022-12-09

How to Cite

Mishura, Y. S., Kushnirenko, S. V., & Voloh, L. V. (2022). Invariant surfaces for certain classes of systems of the second-order to stochastic differential equations with jumps. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (3), 22–27. https://doi.org/10.17721/1812-5409.2022/3.2

Issue

Section

Algebra, Geometry and Probability Theory