Abstract
We study a class of non-densely defined impulsive neutral stochastic functional differential equations driven by an independent cylindrical fractional Brownian motion (fBm) with Hurst parameter H ∈ (1/2, 1) in the Hilbert space. We prove the existence and uniqueness of the integral solution for this kind of equations with the coefficients satisfying some non-Lipschitz conditions. The results are obtained by using the method of successive approximation.
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Ren, Y., Hou, T. & Sakthivel, R. Non-densely defined impulsive neutral stochastic functional differential equations driven by fBm in Hilbert space with infinite delay. Front. Math. China 10, 351–365 (2015). https://doi.org/10.1007/s11464-015-0392-z
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DOI: https://doi.org/10.1007/s11464-015-0392-z
Keywords
- Stochastic functional differential equation
- non-densely defined operator
- cylindrical fractional Brownian motion (fBm)
- impulsive effect