We survey various notions of probabilistic automata and probabilistic bisimulation, accumulating in an expressiveness hierarchy of probabilistic system types. The aim of this paper is twofold: On the one hand it provides an overview of existing types of probabilistic systems and, on the other hand, it explains the relationship between these models. We overview probabilistic systems with discret...

The Schr?dinger differential equation is what we usually solve for the microscopic particles in non-relativistic quantum mechanics. Niels Bohr suggested power two of (usually) complex answer shows probability particle’s existence at a point space. Also, time dependence Schrodinger wave one whereas light electromagnetism two. In this paper, show solution both problems. We derive Wave Equation en...

The concepts of regular generalized functions in Gaussian analysis are presented. Spaces of regular generalized functions are characterized and their probabilistic structure is worked out. Finally, these concepts are applied to a nonlinear (Verhulst type) equation. Its solution is shown to be a regular generalized process with martingale property.

This paper studies a large class of M/C/l queues with vacations. By means of a probabilistic interpretation we obtain a functional equation which gives a unified approach to derive time-dependent results for the workload distribution. We also discuss application of our result to a number vacation models.

In this paper, we try the perceptive analysis of the optimal stopping problem in which both fuzzy and probabilistic uncertainty is accommodated. We establish the recursive equation for computing the expected value of the optimal stopped fuzzy perception reward. Also, a numerical example is given.

A new class of random partial differential equations of parabolic type is considered where the stochastic term consists in an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a prob...

Let p ∈ (1, 2] and β be a nice bounded function. In this article we will analyze the equation (L + β)u = up with analytic and with probabilistic methods. In particular we will give answers to two open problems suggested by Pinsky.

Several approaches to probabilistic design have been proposed in the past. Only few acknowledged the paradigm shift from performance based design to design for cost. The incorporation of economics in the design process, however, makes a probabilistic approach to design necessary, due to the inherent uncertainty of assumptions and the circumstances of operating environments of the future aircraf...

We consider a multidimensional Burgers equation on the torus T and the whole space R . We show that, in case of the torus, there exists a unique global solution in Lebesgue spaces. For a torus we also provide estimates on the large time behaviour of solutions. In the case of R we establish the existence of a unique global solution if a Beale-Kato-Majda type condition is satisfied. To prove thes...

On the basis of integral representations we propose fast numerical methods to solve the Cauchy problem for the stochastic wave equation without boundaries and with the Dirichlet boundary conditions. The algorithms are exact in a probabilistic sense. 1 Statement of the problem and integral representations Consider the stochastic wave equation ∂X ∂t (t, x)− a2 X ∂x (t, x) = g(t, x) + f(t, x) dW (...