STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS DRIVEN BY G-BROWNIAIN MOTION WITH MONOTONE NONLINEARITY

Abstract: By using the Picard iteration scheme, this article establishes the existence and uniqueness theory for solutions to stochastic functional differential equations driven by G-Browniain motion. Assuming the monotonicity conditions, the boundedness and existence-uniqueness results ofsolutions have been derived. The error estimation between Picard approximate solution yk(t) and exact solution y(t) has been determined. The L2G and exponential estimates have been obtained. The theory has been further generalized to weak monotonicity conditions. The existence, uniqueness and exponential estimate under the weak monotonicity conditions have been inaugurated.

Prof. Dr. Faizullah (Faiz) ( Department of Mathematics, Swansea University, United Kingdom )

Prof. Dr. Faizullah (Faiz)

Dr. Faizullah has completed his postdoc from Centro de Investigacin en Matemticas, A.C. (CIMAT) Jalisco S/N Valenciana A.P. 402 36000 Guanajuato, GTO Mexico (North America) and PhD in Applied Mathematics from Ocean University of China. His research interest is stochastic Analysis, Probability Theory, Stochastic Differential equations, Population Dynamics and Finantial Mathematics. He has published more than 40 research publications in international journals. Currently he is working as a professor in Swansea University United Kingdom.