Premium
Optimal controls for second‐order stochastic differential equations driven by mixed‐fractional Brownian motion with impulses
Author(s) -
Dhayal Rajesh,
Malik Muslim,
Abbas Syed,
Debbouche Amar
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6177
Subject(s) - mathematics , stochastic differential equation , fractional brownian motion , uniqueness , brownian motion , geometric brownian motion , stochastic partial differential equation , order (exchange) , differential equation , class (philosophy) , mathematical analysis , diffusion process , computer science , knowledge management , statistics , innovation diffusion , finance , artificial intelligence , economics
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.