International Journal of Stochastic Analysis

List of Papers (Total 1,175)

Cycle times in a starlike network with state-dependent routing

For a star like network (central server system) with state dependent branching we compute the cycle time distribution. The Laplace-Stieltjes transform of this distribution is of product form. This allows to define a recursive algorithm for evaluation of cycle time moments of any order.

On some inventory control problems with state-dependent parameters

This article analyzes discrete Markov processes that arise in some general control problems of a storage (or a dam) with an infinite capacity. Employing a special “step-wise” structure of the transition matrices of these processes, the author obtains conditions for their ergodicity and develops an implementable algorithm for finding the generating function of the corresponding...

Nonlinear boundary value problems for first order impulsive integro-differential equations

In this paper, we investigate a class of first order impulsive integro-differential equations subject to certain nonlinear boundary conditions and prove, with the help of upper and lower solutions, that the problem has a solution lying between the upper and lower solutions. We also develop monotone iterative technique and show the existence of multiple solutions of a class of...

On a multi-channel queue with state dependent input flow and interruptions

This paper deals with a multi-channel queueing system with a finite waiting room but without losses. The latter is achieved by a temporary interruption of the input flow activity until the waiting room is ready to place a new customer. In addition, the input flow on its “busy period” is non-recurrent: It is state dependent and may be controlled over relevant times of decision...

On nonstandard potentials in a Stefan problem

We report some results on nonstandard potentials and their application to solution of the Stefan problem.

Oscillations in linear difference equations with variable coefficients

A class of linear difference equations with variable coefficients is considered. Sufficient conditions and necessary conditions for the oscillation of the solutions are established. In the special cases where the coefficients are constant or periodic the conditions become both necessary and sufficient.

An existence theorem for differential inclusions on Banach space

In this paper we consider the question of existence of solutions for a large class of nonlinear differential inclusions on Banach space arising from control theory.

Properties of solution set of stochastic inclusions

The properties of the solution set of stochastic inclusions xt−xs∈clL2(∫stFτ(xτ)dτ

On applications of Little's formula

In classical Little's formula L=λW used in queueing, the parameter λ serves as the intensity of the input process. In various applications this parameter may not be known. The author discusses important classes of modulated input processes, where this parameter can be found.

Anti-periodic traveling wave solutions to a class of higher-order Kadomtsev-Petviashvili-Burgers equations

We discuss the existence, uniqueness, and continuous dependence on data, of anti-periodic traveling wave solutions to higher order two-dimensional equations of Korteweg-deVries type.

The method of lower and upper solutions for n th-order periodic boundary value problems

In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u(n)(t)=f(t,u(t));u(i)(a)−u(i)(b)=λi∈ℝ,i=0,…,n−1 where f is a Carathéodory function. We obtain sufficient conditions for f to guarantee the existence and approximation of solutions between a lower solution α and an upper solution β for n≥3 with either α≤β or α≥β.


Mean number of real zeros of a random trigonometric polynomial. III

If a1,a2,…,an are independent, normally distributed random variables with mean 0 and variance 1, and if vn is the mean number of zeros on the interval (0,2π) of the trigonometric polynomial a1cosx

Two-parameter semigroups, evolutions and their applications to Markov and diffusion fields on the plane

We study two-parameter coordinate-wise C0-semigroups and their generators, as well as two-parameter evolutions and differential equations up to the second order for them. These results are applied to obtain the Hille-Yosida theorem for homogeneous Markov fields of the Feller type and to establish forward, backward, and mixed Kolmogorov equations for nonhomogeneous diffusion...

On the regularity of many-particle dynamical systems perturbed by white noise

We consider a system of finite number of particles that are moving in Rd under mutual interaction. It is assumed that the particles are subjected to some additional random forces which cause diffusion motion of the particles. The latter is described by a system of stochastic differential equations of the first order for noninertia particles and the second order for inertial...

On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem

In the present paper we study nonlocal problems for ordinary differential equations with a discontinuous coefficient for the high order derivative. We establish sufficient conditions, known as regularity conditions, which guarantee the coerciveness for both the space variable and the spectral parameter, as well as guarantee the completeness of the system of root functions. The...

Existence, uniqueness and continuability of solutions of impulsive differential-difference equations

We consider an initial value problem for impulsive differential-difference equations, and obtain sufficient conditions for the existence, uniqueness, and continuability of solutions of such problem.

The stationary local sojourn time in single server tandem queues with renewal input

We start from an earlier paper evaluating the overall sojourn time to derive the local sojourn time in stationary regime, in a single server tandem queue of (m

Rigorous solution of a mean field spin glass model

A separable spin glass model whose exchange integral takes the form Jij=J(ξi1ξj2

G-H-KKM selections with applications to minimax theorems

Based on the G-H-KKM selections, some nonempty intersection theorems and their applications to minimax inequalities are presented.

Waiting time analysis for MX/G/1 priority queues with/without vacations under random order of service discipline

We study MX/G/1 nonpreemptive and preemptive-resume priority queues with/without vacations under random order of service (ROS) discipline within each class. By considering the conditional waiting times given the states of the system, which an arbitrary message observes upon arrival, we derive the Laplace-Stieltjes transforms of the waiting time distributions and explicitly obtain...

Single server queueing networks with varying service times and renewal input

Using recent results in tandem queues and queueing networks with renewal input, when successive service times of the same customer are varying (and when the busy periods are frequently not broken up in large networks), the local queueing delay of a single server queueing network is evaluated utilizing new concepts of virtual and actual delays (respectively). It appears that...