Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process
The existence and uniqueness of mild solution of an impulsive stochastic system driven by a Rosenblatt process is analyzed in this work by using the Banach fixed point theorem and the theory of resolvent operator developed by R. Grimmer in R. Grimmer, Resolvent operators for integral equations in a...
| Authors: | ; ; ; |
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| Format: | Article |
| Status: | Submitted version |
| Publication date: | 2020 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/100802 |
| Online Access: | https://hdl.handle.net/11441/100802 https://doi.org/10.3934/dcdsb.2019251 |
| Access Level: | Open access |
| Keyword: | Exponential stability Resolvent operator Impulsive neutral stochastic integro-differential equations Rosenblatt process |
| Summary: | The existence and uniqueness of mild solution of an impulsive stochastic system driven by a Rosenblatt process is analyzed in this work by using the Banach fixed point theorem and the theory of resolvent operator developed by R. Grimmer in R. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc., 273 (1982), 333–349. Furthermore, the exponential stability in mean square for the mild solution to neutral stochastic integro-differential equations with Rosenblatt process is obtained by establishing an integral inequality. Finally, an example is exhibited to illustrate the abstract theory. |
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