In this paper we consider Milner's calculus CCS enriched by a probabilistic choice operator. The calculus is given operational semantics based on probabilistic transition systems. We deene operational notions of preorder and equivalence as prob-abilistic extensions of the simulation preorder and the bisimulation equivalence respectively. We extend existing category-theoretic techniques for solv...

In this work we extend Brosamler’s formula (see [2]) and give a probabilistic solution of a non degenerate Poisson type equation with Neumann boundary condition in a bounded domain of the Euclidean space.

We study a class of nonlocal-diffusion equations with drifts, and derive a priori Φ-Hölder estimate for the solutions by using a purely probabilistic argument, where Φ is an intrinsic scaling function for the equation.

Probabilistic functional equations have been used to analyze various models in computational biology and learning theory. It is worth noting that they are linked the symmetry of a system equations’ transformation. Our objective propose generic probabilistic equation can cover most mathematical addressed existing literature. The notable fixed-point tools utilized examine existence, uniqueness, s...

In this paper, we give a probabilistic counterpart of  Mazur-Ulam theorem  in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.

Using a probabilistic risk-based framework, we have developed a simple predictive risk threshold model for protecting the survival of farmed abalone, Haliotis diversicolor supertexta, exposed to waterborne zinc (Zn). Probabilistic techniques using Monte Carlo analysis propagate parameter uncertainty/variability throughout the model, providing decision makers with a credible range of information...

We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the viscosity sense. We treat open state constraints as a special case of expecta...

It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of an infinite continued fraction. We examine the probabilistic significance of the expansion. To illustrate our results, we discuss some examples of ...

We prove a general Ulam-Hyers stability theorem for a nonlinear equation in probabilistic metric spaces, which is then used to obtain stability properties for different kinds of functional equations linear functional equations, generalized equation of the square root, spiral generalized gamma equations in random normed spaces. As direct and natural consequences of our results, we obtain general...

In this work, we begin by considering the qualitative modeling of biological regulatory systems using process hitting, from which we define its probabilistic counterpart by considering the chemical master equation within a kinetic theory framework. The last equation is efficiently solved by considering a separated representation within the proper generalized decomposition framework that allows ...