In this paper, we give a kind of Cauchy 1-completeness in probabilistic quasi-uniform spaces by using 1-filters. Utilizingthe relationships among probabilistic quasi-uniformities, classical quasi-uniformities and Hutton [0, 1]-quasi-uniformities,we show the relationships between their completeness. In fuzzy quasi-metric spaces, we establish the relationshipsbetween the completeness of induced p...

We provide probabilistic representations of the solution some semilinear hyperbolic and high-order PDEs based on branching diffusions. These pave way for an approximation by standard Monte Carlo method, whose error estimate is controlled central limit theorem, thus partly bypassing curse dimensionality. illustrate numerical implications in context popular physics such as nonlinear Klein–Gordon ...

We consider the problem of computing reachability probabilities: given a Markov chain, an initial state of the Markov chain, and a set of goal states of the Markov chain, what is the probability of reaching any of the goal states from the initial state? This problem can be reduced to solving a linear equation A · x = b for x, where A is a matrix and b is a vector. We consider two iterative meth...

We investigate a stochastic evolution equation for the motion of a second grade fluid filling a bounded domain of R. Global existence and uniqueness of strong probabilistic solution is established. In contrast to previous results on this model we show that the sequence of Galerkin approximation converges in mean square to the exact strong probabilistic solution of the problem. We also give two ...

In this paper, we introduce a probabilistic numerical scheme for a class of parabolic and elliptic fully non-linear PDEs in bounded domains. In the main result, we provide the convergence of a discrete-time approximation to the viscosity solution of a fully non-linear parabolic equation by assuming that comparison principle holds for the PDE.

The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...

Cognitive neuroscientists of language comprehension study how neural computations relate to cognitive computations during comprehension. On the cognitive part of the equation, it is important that the computations and processing complexity are explicitly defined. Probabilistic language models can be used to give a computationally explicit account of language complexity during comprehension. Whe...

The quantitative analysis of concurrent systems requires expressive and user-friendly property languages combining temporal, datahandling, and quantitative aspects. In this paper, we aim at facilitating the quantitative analysis of systems modeled as PTSs (Probabilistic Transition Systems) labeled by actions containing data values and probabilities. We propose a new regular probabilistic operat...