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Volume 32, Issue 2
Sobolev-type Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion with Non-Lipschitz Coefficients

Wentao Zhan & Zhi Li

DOI: 10.4208/jpde.v32.n2.4

J. Part. Diff. Eq., 32 (2019), pp. 144-155.

Published online: 2019-07

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  • Abstract

In this paper, we are concerned with the existence and uniqueness of mild solution for a class of nonlinear fractional Sobolev-type stochastic differential equations driven by fractional Brownian motion with Hurst parameter H∈(1/2,1) in Hilbert space. We obtain the required result by using semigroup theory, stochastic analysis principle, fractional calculus and Picard iteration techniques with some non-Lipschitz conditions.

  • Keywords

Fractional Sobolev-type stochastic differential equations fractional Brownian motion mild solution.

  • AMS Subject Headings

60H15, 26A33, 60G15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lizhi_csu@126.com (Zhi Li)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-32-144, author = {Zhan , Wentao and Li , Zhi}, title = {Sobolev-type Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion with Non-Lipschitz Coefficients}, journal = {Journal of Partial Differential Equations}, year = {2019}, volume = {32}, number = {2}, pages = {144--155}, abstract = {

In this paper, we are concerned with the existence and uniqueness of mild solution for a class of nonlinear fractional Sobolev-type stochastic differential equations driven by fractional Brownian motion with Hurst parameter H∈(1/2,1) in Hilbert space. We obtain the required result by using semigroup theory, stochastic analysis principle, fractional calculus and Picard iteration techniques with some non-Lipschitz conditions.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v32.n2.4}, url = {http://global-sci.org/intro/article_detail/jpde/13239.html} }
TY - JOUR T1 - Sobolev-type Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion with Non-Lipschitz Coefficients AU - Zhan , Wentao AU - Li , Zhi JO - Journal of Partial Differential Equations VL - 2 SP - 144 EP - 155 PY - 2019 DA - 2019/07 SN - 32 DO - http://doi.org/10.4208/jpde.v32.n2.4 UR - https://global-sci.org/intro/article_detail/jpde/13239.html KW - Fractional Sobolev-type stochastic differential equations KW - fractional Brownian motion KW - mild solution. AB -

In this paper, we are concerned with the existence and uniqueness of mild solution for a class of nonlinear fractional Sobolev-type stochastic differential equations driven by fractional Brownian motion with Hurst parameter H∈(1/2,1) in Hilbert space. We obtain the required result by using semigroup theory, stochastic analysis principle, fractional calculus and Picard iteration techniques with some non-Lipschitz conditions.

Zhan , Wentao and Li , Zhi. (2019). Sobolev-type Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion with Non-Lipschitz Coefficients. Journal of Partial Differential Equations. 32 (2). 144-155. doi:10.4208/jpde.v32.n2.4
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