In this paper we study monotonicity results for optimal policies of various queueing and resource sharing models. The standard approach is to propagate, for each speciic model, certain properties of the dynamic programming value function. By concentrating on the events and the properties instead of on the value function we propose a uniied treatment of monotonicity results for Markovian models....

Motivated by applications in mathematical finance [3] and stochastic analysis [16], we continue our study of second order backward stochastic equations (2BSDE). In this paper, we derive the dynamic programming equation for a certain class of problems which we call as the second order stochastic target problems. In contrast with previous formulations of similar problems, we restrict control proc...

We introduce a rapid grid search method in solving the dynamic programming problems in economics. Compared to mainstream grid search methods, by using local information of the Bellman equation, this method can significantly increase the efficiency in solving dynamic programming problems by reducing the grid points searched in the control space.

Abstract We prove that the solutions to discrete nonlinear Schrödinger equation with non-local algebraically decaying coupling converge strongly in $$L^2({\mathbb {R}}^2)$$ L 2 ( R ) those of cont...

For systems of coupled differential equations on a sequence of W -random graphs, we derive the continuum limit in the form of an evolution integral equation. We prove that solutions of the initial value problems (IVPs) for the discrete model converge to the solution of the IVP for its continuum limit. These results combined with the analysis of nonlocally coupled deterministic networks in Medve...

In this paper static and dynamic response of nanotweezers composed of two carbon nanotube (CNT) arms are investigated. Taking into account a continuum model and considering the electrostatic actuation as well as the presence of the van der Waals forces, the static nonlinear equations are solved by a step by step linearization and Galerkin projection method. Simulating the closing dynamics of a ...

In this talk, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to minimize the instantaneous travel cost to the destination. The density is governed by a conservation law whereas the minimization principle is described by a gra...