STOCHASTIC CENTER OF SYSTEMS OF STOCHASTIC DIFFERENTIAL EQUATIONS ON THE PLANE

Guoting Chen; Changjian Liu

doi:10.11948/2017005

2017 Volume 7 Issue 1

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Guoting Chen, Changjian Liu. STOCHASTIC CENTER OF SYSTEMS OF STOCHASTIC DIFFERENTIAL EQUATIONS ON THE PLANE[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 67-78. doi: 10.11948/2017005

Citation:

Guoting Chen, Changjian Liu. STOCHASTIC CENTER OF SYSTEMS OF STOCHASTIC DIFFERENTIAL EQUATIONS ON THE PLANE[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 67-78. doi: 10.11948/2017005

STOCHASTIC CENTER OF SYSTEMS OF STOCHASTIC DIFFERENTIAL EQUATIONS ON THE PLANE

Guoting Chen¹,
Changjian Liu²

1 UFR de Mathématiques, Laboratoire Paul Painlevé, Université de Lille 1, 59655 Villeneuve d'Ascq, France;
2 School of Mathematics, Soochow University, 215006 Suzhou, China

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Abstract

Abstract

We study a stochastic analogy of the famous center problem of Dulac for quadratic differential equations in the plane. We introduce the concept of center for systems of stochastic differential equations of Itô's type on the plane, called stochastic center. We derive a criterion for the existence of such a center. We apply it to obtain necessary and sufficient conditions for quadratic stochastic differential equations in dimension 2.
- Center conditions /
- stochastic differential equations
MSC: 34C05;60H10

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References

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