Band 34, Heft 1

In this paper, we are concerned with an optimal control problem where the system is driven by a G-stochastic differential equation. Using the associated adjoint equation, where an admissible set of controls is convex, we establish necessary as well as sufficient optimality conditions for relaxed controls.

The paper presents the dynamical analysis of an avian influenza infection model in birds population with half-saturated incidence. The positivity of solutions is proved by the occurrence of a global positive solution. Also, we analyze the extinction scenario of infection under certain parametric restriction. Moreover, we define the reproduction ratio R 0 S R_{0}^{S} to examine the stochastic stability through the stationary distribution. In order to figure out when infection appears in the birds population and when it stops the spread, we derive the condition on R 0 S R_{0}^{S} . Furthermore, we generate some graphical simulations to support the theoretical results based on the value of reproduction ratio.

In this paper, we investigate doubly reflected generalized backward stochastic differential equations with two reflecting right-continuous with left-limited barriers in a general filtration supporting a Brownian motion and an independent integer-valued random measure. We establish the existence and uniqueness of the solution when the barriers and their left limits are completely separated without assuming Mokobodski’s hypothesis or the regularity condition.

In this paper, we study the existence and the uniqueness of optional solutions of stochastic differential equations with respect to optional semimartingales by using a successive approximation method under a non-Lipschitz condition. The stability of solutions to non-Lipschitz SDEs is also considered, and the stochastic stability is obtained in the sense of mean square.

The consistency of the estimator G 55 {G_{55}} for quadratic forms of the regularized inverse covariance matrix is proven.