International Journal of Stochastic Analysis

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

List of Papers (Total 36)

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...

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...

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.

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.

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...

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...

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...

Linear distribution processes

In this paper, we propose a generalization of continuous-time processed defined by Xt=∫f(t−s)dWs, to the case of f being a distribution. We give a necessary and sufficient condition for f, such that the obtained process is a second order distribution process. We study the moments and the regularity of these processes. In addition, we investigate a generalization to processes with...

On certain random polygons of large areas

Consider the tesselation of a plane into convex random polygons determined by a unit intensity Poissonian line process. Let M(A) be the ergodic intensity of random polygons with areas exceeding a value A. A two-sided asymptotic bound exp{−2A/π

Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem

The aim of this paper is to investigate the existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem in a general Banach space. For this purpose, a special kind of a mild solution is introduced and the Banach contraction theorem and a modified Picard method are applied.

Robust option replication for a Black-Scholes model extended with nondeterministic trends

Statistical analysis on various stocks reveals long range dependence behavior of the stock prices that is not consistent with the classical Black and Scholes model. This memory or nondeterministic trend behavior is often seen as a reflection of market sentiments and causes that the historical volatility estimator becomes unreliable in practice. We propose an extension of the...

On the stabilization of the energy of a harmonic oscillator disturbed by random processes of the “white and shot noises” types

In this paper the behavior of the instantaneous energy of a harmonic oscillator is investigated in the case when at a certain angle to the vector of the phase velocity of the oscillator, random disturbances of the “white and shot noises” types are acting.

Parallelization algorithms for modeling ARM processes

AutoRegressive Modular (ARM) processes are a new class of nonlinear stochastic processes, which can accurately model a large class of stochastic processes, by capturing the empirical distribution and autocorrelation function simultaneously. Given an empirical sample path, the ARM modeling procedure consists of two steps: a global search for locating the minima of a nonlinear...

Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs

Linear-implicit versions of strong Taylor numerical schemes for finite dimensional Itô stochastic differential equations (SDEs) are shown to have the same order as the original scheme. The combined truncation and global discretization error of an γ strong linear-implicit Taylor scheme with time-step Δ applied to the N dimensional Itô-Galerkin SDE for a class of parabolic...

Tree-indexed processes: a high level crossing analysis

Consider a branching diffusion process on R1 starting at the origin. Take a high level u>0 and count the number R(u,n) of branches reaching u by generation n. Let Fk,n(u) be the probability P(R(u,n)<k),k=1,2,…. We study the limit limn→∞Fk,n(u)=Fk(u). More precisely, a natural equation for the probabilities Fk(u) is introduced and the structure of the set of solutions is analysed...

On the time of the maximum of Brownian motion with drift

The distribution of the time at which Brownian motion with drift attains its maximum on a given interval is obtained by elementary methods. The proof depends on a remarkable integral identity involving Gaussian distribution functions.

A note of stability of weakly efficient solution set for optimization with set-valued maps

In this paper, we study the stability of weakly efficient solution sets for optimization problems with set-valued maps. We introduce the concept of essential weakly efficient solutions and essential components of weakly efficient solution sets. We first show that most optimization problems with set-valued maps (in the sense of Baire category) are stable. Secondly, we obtain some...

The Pólya-Aeppli process and ruin problems

The Pólya-Aeppli process as a generalization of the homogeneous Poisson process is defined. We consider the risk model in which the counting process is the Pólya-Aeppli process. It is called a Pólya-Aeppli risk model. The problem of finding the ruin probability and the Cramér-Lundberg approximation is studied. The Cramér condition and the Lundberg exponent are defined. Finally...

Itô-Skorohod stochastic equations and applications to finance

We prove an existence and uniqueness theorem for a class of Itô-Skorohod stochastic equations. As an application, we introduce a Black-Scholes market model where the price of the risky asset follows a nonadapted equation.