Solvability and optimal controls of non-instantaneous impulsive stochastic neutral integro-differential equation driven by fractional Brownian motion. (English) Zbl 1484.34179
Summary: In this manuscript, a new class of non-instantaneous impulsive stochastic neutral integrodi fferential equation driven by fractional Brownian motion (fBm, in short) with state-dependent delay and their stochastic optimal control problem is studied. We utilize the theory of the resolvent operator and a fixed point technique to present the solvability of the stochastic system. Then, the existence of optimal controls is discussed for the proposed stochastic system. Finally, an example is offered to demonstrate the obtained theoretical results.
MSC:
| 34K45 | Functional-differential equations with impulses |
| 34K40 | Neutral functional-differential equations |
| 34K43 | Functional-differential equations with state-dependent arguments |
| 49J55 | Existence of optimal solutions to problems involving randomness |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 93E20 | Optimal stochastic control |
Keywords:
stochastic neutral integro-differential equation; optimal controls; state-dependent delay; fractional Brownian motion; non-instantaneous impulsesReferences:
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