We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local eigenvalue behavior. The stochastic Airy operator displays soft edge behavior, associated with the Airy kernel. The stochastic Bessel operator displays hard edge...

The synthesis of stochastic finite-state automata is possible using two kinds of components-deterministic finite-state automata and ergodic signal generators. The starting point in such a synthesis methods is a decomposition of stochastic matrix, its representation as a linear form of simple matrices which belong to the class of transition matrices of deterministic automata. New heuristic crite...

We study here the discretization by monotone finite volume schemes of multi-dimensional nonlinear scalar conservation laws forced by a multiplicative noise with a time and space dependent flux-function and a given initial data in L(R). After establishing the well-posedness theory for solutions of such kind of stochastic problems, we prove under a stability condition on the time step the converg...

We consider finite-population and finite-capacity polling systems. The behavior of these systems is described by means of generalized stochastic Petri nets. The exact results for the mean response times are obtained numerically by means of the stochastic Petri net package. Finite population polling systems are generally difficult to analyze. Thus, one of the contributions of this paper is the f...

in this research, an innovative numerical simulating approach for time domain analysis of multi degrees of freedom structures with uncertainty in dynamic properties is presented. a full scale finite element model of multi-story and multi bays of three sample structures has been constructed. the reduced order model of structure with holding the dominant and effective gramians in the balanced sta...

An infinite-horizon, stochastic model of entry and exit with sunk costs and imperfect competition is constructed. A subgame perfect Nash equilibrium for the general dynamic stochastic game is shown to exist as a limit of finite-horizon equilibria. This equilibrium has a relatively simple structure characterized by two numbers per finite history. Under very general conditions, it tends to exhibi...

In this paper, European option pricing with stochastic volatility forecasted by well known GARCH model is discussed in context of Indian financial market. The data of Reliance Ltd. stockprice from 3/01/2000 to 30/03/2009 is used and resulting partial differential equation is solved byCrank-Nicolson finite difference method for various interest rates and maturity in time. Thesensitivity measures...

Stochastic switched systems are a relevant class of stochastic hybrid systems with probabilistic evolution over a continuous domain and control-dependent discrete dynamics over a finite set of modes. In the past few years several different techniques have been developed to assist in the stability analysis of stochastic switched systems. However, more complex and challenging objectives related t...

Abstract: This paper investigates the problem of global finite-time stabilization by state feedback for a class of stochastic nonlinear systems with low-order nonlinearities, to which the existing control methods are inapplicable. By skillfully adopting the method of adding a power integrator and constructing twice continuous differential Lyapunov functions, a stepwise constructive continuous s...

In this paper, the finite horizon H∞ control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of sampled-data measurements. The methodology adopted involves a certain equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, by solving the finite horizon H∞ control problem for the equivalent stochastic problem ...