Geodesic
Approximate controllability of impulsive stochastic systems driven by Rosenblatt process and Brownian motion
Ural mathematical journal, Tome 8 (2022) no. 2, pp. 59-70

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In this paper we consider a class of impulsive stochastic functional differential equations driven simultaneously by a Rosenblatt process and standard Brownian motion in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the approximate controllability for the mild solution by means of the Banach fixed point principle. At the end we provide a practical example in order to illustrate the viability of our result.
Keywords: approximate controllability, fixed point theorem, Rosenblatt process, mild solution stochastic impulsive systems. 
@article{UMJ_2022_8_2_a4,
     author = {Abbes Benchaabane},
     title = {Approximate controllability of impulsive stochastic systems driven by {Rosenblatt} process and {Brownian} motion},
     journal = {Ural mathematical journal},
     pages = {59--70},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a4/}
}
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Abbes Benchaabane. Approximate controllability of impulsive stochastic systems driven by Rosenblatt process and Brownian motion. Ural mathematical journal, Tome 8 (2022) no. 2, pp. 59-70. http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a4/