arXiv subjects

Faiz Faizullah

Publications and source records attributed to Faiz Faizullah.

4 recordsLinked to original sources

arXiv2020

On the existence-uniqueness and exponential estimate for solutions to stochastic functional differential equations driven by G-L\'evy process

The existence-uniqueness theory for solutions to stochastic dynamic systems is always a significant theme and has received a huge attention. The objective of this article is to study the mentioned theory for stochastic functional differential equations (SFDEs) driven by G-L\'evy process. The existence-uniqueness theorem for solutions to SFDEs driven by G-L\'evy process has been determined. The error estimation between the exact solution and Picard approximate solutions has been shown. In addition, the exponential estimate has been derived.

math.PR↗

arXiv2018

Estimates for the difference between approximate and exact solutions to stochastic differential equations in the G-framework

This article investigates the Euler-Maruyama approximation procedure for stochastic differential equations in the framework of G-Browinian motion with non-linear growth and non-Lipschitz conditions. Subject to non-linear growth condition, it is revealed that the Euler-Maruyama approximate solutions are bounded in M^2_G.In view ofnon-linear growth and non-uniform Lipschitz conditions,we give estimates for the difference between the exact solution Z(t) and approximate solutions Zq(t) of SDEs in the framework of G-Brownia nmotion.

math.PR↗

arXiv2018

Stochastic functional differential equations driven by G-Browniain motion with monotone nonlinearity

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 of solutions have been derived. The error estimation between Picard approximate solution $y^k(t)$ and exact solution $y(t)$ has been determined. The $L^2_G$ 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.

math.PR↗

arXiv2018

Existence and asymptotic properties for the solutions to nonlinear SFDEs driven by G-Brownian motion with infinite delay

The aim of this paper is to present the analysis for the solutions of nonlinear stochastic functional differential equation driven by G-Brownian motion with infinite delay (G-SFDEwID). Under some useful assumptions, we have proved that the G-SFDEwID admits a unique local solution. The mentioned theory has been further generalized to show that G-SFDEwID admits a unique strong global solution. The asymptotic properties, mean square boundedness and convergence of solutions with different initial data have been derived. We have assessed that the solution map $X_t$ is mean square bounded and two solution maps from different initial data are convergent. In addition, the exponential estimate for the solution has been studied.

math.PR↗