arXiv subjects

Syed Abbas

Publications and source records attributed to Syed Abbas.

21 records · Page 2Linked to original sources

arXiv2013

A general maximum principle for mean-field stochastic differential equations with jump processes

In this paper, we investigate the optimal control problems for stochastic differential equations (SDEs in short) of mean-field type with jump processes. The control variable is allowed to enter into both diffusion and jump terms. This stochastic maximum principle differs from the classical one in the sense that here the first-order adjoint equation turns out to be a linear mean-field backward SDE with jumps, while the second-order adjoint equation remains the same as in Tang and Li's stochastic maximum principle [32]. Finally, for the reader's convenience we give some analysis results used in this paper in the Appendix.

math.OC↗

arXiv2012

Analysis of Caputo impulsive fractional order differential equations with applications

We use Sadavoskii's fixed point method to investigate the existence and uniqueness of solutions of Caputo impulsive fractional differential equations of order αbetween 0 and 1 with one example of impulsive logistic model and few other examples as well. We also discuss Caputo impulsive fractional differential equations with finite delay. The results proven are new and complement the existing one.

math.CA↗

arXiv2011

On Necessary and Sufficient Conditions for Near-Optimal Singular Stochastic Controls

This paper is concerned with necessary and sufficient conditions for near-optimal singular stochastic controls for systems driven by a nonlinear stochastic differential equations (SDEs in short). The proof of our result is based on Ekeland's variational principle and some delicate estimates of the state and adjoint processes. This result is a generalization of Zhou's stochastic maximum principle for near-optimality to singular control problem.

math.OC↗