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Volume 31, Issue 2
Neutral Fractional Stochastic Differential Equations Driven by Rosenblatt Process

Liping Xu & Zhi Li

DOI: 10.4208/jpde.v31.n2.3

J. Part. Diff. Eq., 31 (2018), pp. 159-176.

Published online: 2018-07

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  • Abstract

In this paper, we are concerned with a class of neutral fractional stochastic partial differential equations driven by a Rosenblatt process. By the stochastic analysis technique, the properties of operator semigroup and combining the Banach fixed-point theorem, we prove the existence and uniqueness of the mild solutions to this kind of equations driven by Rosenblatt process. In the end, an example is given to demonstrate the theory of our work.

  • Keywords

Fractional neutral SDEs Rosenblatt process existence and uniqueness.

  • AMS Subject Headings

60H15, 60G15, 60H05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xlp211@126.com (Liping Xu)

lizhi_csu@126.com (Zhi Li)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-31-159, author = {Xu , Liping and Li , Zhi}, title = {Neutral Fractional Stochastic Differential Equations Driven by Rosenblatt Process}, journal = {Journal of Partial Differential Equations}, year = {2018}, volume = {31}, number = {2}, pages = {159--176}, abstract = {

In this paper, we are concerned with a class of neutral fractional stochastic partial differential equations driven by a Rosenblatt process. By the stochastic analysis technique, the properties of operator semigroup and combining the Banach fixed-point theorem, we prove the existence and uniqueness of the mild solutions to this kind of equations driven by Rosenblatt process. In the end, an example is given to demonstrate the theory of our work.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n2.3}, url = {http://global-sci.org/intro/article_detail/jpde/12515.html} }
TY - JOUR T1 - Neutral Fractional Stochastic Differential Equations Driven by Rosenblatt Process AU - Xu , Liping AU - Li , Zhi JO - Journal of Partial Differential Equations VL - 2 SP - 159 EP - 176 PY - 2018 DA - 2018/07 SN - 31 DO - http://doi.org/10.4208/jpde.v31.n2.3 UR - https://global-sci.org/intro/article_detail/jpde/12515.html KW - Fractional neutral SDEs KW - Rosenblatt process KW - existence and uniqueness. AB -

In this paper, we are concerned with a class of neutral fractional stochastic partial differential equations driven by a Rosenblatt process. By the stochastic analysis technique, the properties of operator semigroup and combining the Banach fixed-point theorem, we prove the existence and uniqueness of the mild solutions to this kind of equations driven by Rosenblatt process. In the end, an example is given to demonstrate the theory of our work.

Liping Xu & Zhi Li. (2019). Neutral Fractional Stochastic Differential Equations Driven by Rosenblatt Process. Journal of Partial Differential Equations. 31 (2). 159-176. doi:10.4208/jpde.v31.n2.3
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