Abstract. We consider a class of nonlinear partial-differential equations, including the spatially homogeneous Fokker-Planck-Landau equation for Maxwell (or pseudo-Maxwell) molecules. Continuing the work of [6, 7, 4], we propose a probabilistic interpretation of such a P.D.E. in terms of a nonlinear stochastic differential equation driven by a standard Brownian motion. We derive a numerical sch...

The complex measure condition was introduced by Itô (1965) as a sufficient condition on the potential term in a one-dimensional Schrödinger equation and/or corresponding linear diffusion equation to obtain a FeynmanKac path integral formula. In this paper we provide an alternative probabilistic derivation of this condition and extend it to include any other lower order terms, i.e. drift and for...

This paper presents a mu-calculus-based modal logic for describing properties of reactive probabilistic labeled transition systems (RPLTSs) and develops a modelchecking algorithm for determining whether or not states in finite-state RPLTSs satisfy formulas in the logic. The logic is based on the distinction between (probabilistic) “systems” and (nonprobabilistic) “observations”: using the modal...

This work is devoted to the formal verification of specifications over general discrete-time Markov processes, with an emphasis on infinite-horizon properties. These properties, formulated in a modal logic known as PCTL, can be expressed through value functions defined over the state space of the process. The main goal is to understand how structural features of the model (primarily the presenc...

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...