Optimal controls for second‐order stochastic differential equations driven by mixed‐fractional Brownian motion with impulses

By Rajesh Dhayal, Muslim Malik, Syed Abbas, Amar Debbouche. Mathematical methods in the applied sciences, 2020

102 citations recorded by the source corpus.

We study optimal control problems for a class of second‐order stochastic differential equation driven by mixed‐fractional Brownian motion with non‐instantaneous impulses. By using stochastic analysis theory, strongly continuous cosine family, and a fixed point approach, we establish the existence of mild solutions for the stochastic system. Moreover, the optimal control results are derived without uniqueness of mild solutions of the stochastic system. Finally, the main results are validated with the aid of an example.

Subfields: Applied Mathematics, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/c5905e3fb865f4ce304dab092755aa0e55ce660c

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In Applied Mathematics

1. Rajesh Dhayal
2. Muslim Malik
3. Syed Abbas

In Modeling and Simulation

1. Rajesh Dhayal
2. Muslim Malik
3. Syed Abbas

Citations in the corpus

• Approximate and trajectory controllability of fractional stochastic differential equation with non‐instantaneous impulses and Poisson jumps (2020, background): “It has many interesting properties, such as stationary increments, self-similarity, and long-range dependence properties when H>1=2: For more details on fBm, see [9-12] and the references cited therein.”