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

Yu. S. Mishura; S. V. Kushnirenko; L. V. Voloh

doi:10.17721/1812-5409.2022/3.2

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

Authors

Yu. S. Mishura Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-6877-1800
S. V. Kushnirenko Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-8390-5870
L. V. Voloh Kyiv National University of Technologies and Design https://orcid.org/0000-0002-4290-795X

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

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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.

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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. Series: Physics and Mathematics, (3), 22–27. https://doi.org/10.17721/1812-5409.2022/3.2

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Issue

No. 3 (2022)

Section

Algebra, Geometry and Probability Theory

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