A class of second-order McKean-Vlasov stochastic evolution equations driven by fractional Brownian motion and Poisson jumps

被引：5

作者：

McKibben, Mark A. ^{[1
]}

Webster, Micah ^{[2
]}

机构：

[1] West Chester Univ, Dept Math, 25 Univ Ave, W Chester, PA 19383 USA

[2] Goucher Coll, Ctr Data Math & Computat Sci, 1021 Dulaney Valley Rd, Baltimore, MD 21204 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2020年 / 79卷 / 02期

关键词：

Stochastic evolution equation; McKean-Vlasov; Fractional Brownian motion; Second-order equation; Poisson jumps; Cosine family; DIFFERENTIAL-EQUATIONS; DIFFUSION; EXISTENCE; DELAY;

D O I：

10.1016/j.camwa.2019.07.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper focuses on a class of second-order McKean-Vlasov stochastic evolution equations driven by a fractional Brownian motion and Poisson jumps. Specifically, we allow nonlinearities and the jump term to depend not only of the state of the solution, but also on the corresponding probability law of the state. The global existence and uniqueness of mild solutions is established under various growth conditions, and a related stability result is discussed. An example is presented to illustrate the applicability of the theory. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：391 / 406

页数：16

共 37 条

[31]

McKibben MA., 2004, J Appl Math Stoch Anal, V2, P177

[32] DIFFUSION WITH INTERACTIONS AND COLLISIONS BETWEEN COLORED PARTICLES AND THE PROPAGATION OF CHAOS [J].

NAGASAWA, M ;

TANAKA, H .

PROBABILITY THEORY AND RELATED FIELDS, 1987, 74 (02) :161-198

[33]

Nagy B., 1976, Period. Math. Hungar., V7, P213

[34] Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps [J].

Palanisamy, Muthukumar ;

Chinnathambi, Rajivganthi .

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2015, 28 (05) :1033-1048

[35] Existence, uniqueness, and stability of mild solutions for second-order neutral stochastic evolution equations with infinite delay and Poisson jumps [J].

Ren, Yong ;

Sakthivel, R. .

JOURNAL OF MATHEMATICAL PHYSICS, 2012, 53 (07)

[36] COSINE FAMILIES AND ABSTRACT NON-LINEAR 2ND ORDER DIFFERENTIAL-EQUATIONS [J].

TRAVIS, CC ;

WEBB, GF .

ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1978, 32 (1-2) :75-96

[37]

Travis CC., 1977, HOUSTON J MATH, V3, P555, DOI DOI 10.1007/BF00992842

← 1 2 3 4 →