International Journal of Stochastic Analysis

https://www.hindawi.com/journals/ijsa/

List of Papers (Total 148)

On Rayleigh waves in a thinly layered laminated thermoelastic medium with stress couples under initial stresses

A study is made of the propagation of Rayleigh waves in a thinly layered laminated thermoelastic medium under deviatoric, hydrostatic, and couple stresses. The frequency equation of the Rayleigh waves is obtained. The phase velocity of the Rayleigh waves depends on the initial stress, deviatoric stress, and the couple stress. The laminated medium is first replaced by an...

Editorial

On Markovian traffic with applications to TES processes

Markov processes are an important ingredient in a variety of stochastic applications. Notable instances include queueing systems and traffic processes offered to them. This paper is concerned with Markovian traffic, i.e., traffic processes whose inter-arrival times (separating the time points of discrete arrivals) form a real-valued Markov chain. As such this paper aims to extend...

Mean time for the development of large workloads and large queue lengths in the GI/G/1 queue

We consider the GI/G/1 queue described by either the workload U(t) (unfinished work) or the number of customers N(t) in the system. We compute the mean time until U(t) reaches excess of the level K, and also the mean time until N(t) reaches N0. For the M/G/1 and GI/M/1 models, we obtain exact contour integral representations for these mean first passage times. We then compute the...

A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation

We use the path-valued process called the “Brownian snake” to investigate the trace at the boundary of nonnegative solutions of a semilinear parabolic partial differential equation. In particular, we characterize possible traces and in dimension one we prove that nonnegative solutions are in one-to-one correspondence with their traces at the origin. We also provide probabilistic...

Reduction of differentiable equations with impulse effect

We consider a problem of a partial linearization of noninvertible differential equations with impulse effect and establish sufficient conditions for the dynamical equivalence.

Performance limitations of parallel simulations

This study shows how the performance of a parallel simulation may be affected by the structure of the system being simulated. We consider a wide class of “linearly synchronous” simulations consisting of asynchronous and synchronous parallel simulations (or other distributed-processing systems), with conservative or optimistic protocols, in which the differences in the virtual...

Julian Keilson

The strict stability of dynamic systems on time scales

The strict stability of dynamic systems on time scales is examined with sufficient conditions. Results analogous to Lyapunov's theorems ae proved and discussed using a comparison principle.

On a multi-channel transportation loss system with controlled input and controlled service

A multi-channel loss queueing system is investigated. The input stream is a controlled point process. The service in each of m parallel channels depends on the state of the system at certain moments of time when input and service may be controlled. To obtain explicitly the limiting distribution of the main process (Zt) (the number of busy channels) in equilibrium, an auxiliary...

Surface integrals approach to solution of some free boundary problems - II

This paper is a continuation of the publication [1] where integral equation techniques were applied to the solution of a generalized Stefan problem. The regularization of the corresponding system of nonlinear integral Volterra equations offered here is quite different from that in [1], hence - several new algorithms and numerical experiments. For consistency and easy reference we...

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...

Boundaries in digital planes

The importance of topological connectedness properties in processing digital pictures is well known. A natural way to begin a theory for this is to give a definition of connectedness for subsets of a digital plane which allows one to prove a Jordan curve theorem. The generally accepted approach to this has been a non-topological Jordan curve theorem which requires two different...

The non-parameter penalty function method in constrained optimal control problems

This paper is concerned with the generalization, numerical implementation and testing of the non-parameter penalty function algorithm which was initially developed for solving n-dimensional optimization problems. It uses this method to transform a constrained optimal control problem into a sequence of unconstrained optimal control problems. It is shown that the solutions to the...

Impulsive nonlocal nonlinear parabolic differential problems

The aim of the paper is to prove a theorem about a weak impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities. A weak maximum principle for an impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities and an uniqueness criterion for the existence of the classical...

Laws of large numbers for L-statistics

Consider Ln=n−1∑1≤i≤ncnig(Xn:i) for order statistics Xn:i and let cni=n∫(i−1)/ni/nJdλ for some (Lebesgue) λ-summable over (0,1) function J. Sufficient as well as necessary conditions for limnLn=∫01Jgdλ to hold almost surely and in probability are given. Superposition (or Nemytskii) operators have been used to derive the laws of large numbers for L-statistics from the laws of...

A system of impulsive degenerate nonlinear parabolic functional-differential inequalities

A theorem about a system of strong impulsive degenerate nonlinear parabolic functional-differential inequalities in an arbitrary parabolic set is proved. As a consequence of the theorem, some theorems about impulsive degenerate nonlinear parabolic differential inequalities and the uniqueness of a classical solution of an impulsive degenerate nonlinear parabolic differential...

Brownian local times

In this paper explicit formulas are given for the distribution functions and the moments of the local times of the Brownian motion, the reflecting Brownian motion, the Brownian meander, the Brownian bridge, the reflecting Brownian bridge and the Brownian excursion.

On certain classes of variational inequalities and related iterative algorithms

In this paper, we introduce and study some new classes of variational inequalities and Wiener-Hopf equations. Essentially using the projection technique, we establish the equivalence between the multivalued general quasi-variational inequalities and the multivalued implicit Wiener-Hopf equations. This equivalence enables us to suggest and analyze a number of iterative algorithms...

A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation

We use the path-valued process called the “Brownian snake” to investigate the trace at the boundary of nonnegative solutions of a semilinear parabolic partial differential equation. In particular, we characterize possible traces and in dimension one we prove that nonnegative solutions are in one-to-one correspondence with their traces at the origin. We also provide probabilistic...

The failure rate in reliability: approximations and bounds

We consider models typical to the area of reliability, and a failure rate function for processes describing the dynamics of these models. Various approximations of the failure rate function are proposed and their accuracies are investigated. The basic case studied in the paper is a regenerative model. Some interesting particular cases (Markov, semi-Markov, etc.) are considered...