We use the fixed point method to prove the probabilistic Hyers–Ulam and generalized Hyers–Ulam–Rassias stability for the nonlinear equation f (x) = Φ(x, f (η(x))) where the unknown is a mapping f from a nonempty set S to a probabilistic metric space (X ,F,TM) and Φ : S×X → X , η : S → X are two given functions. Mathematics subject classification (2000): 39B52, 39B82, 47H10, 54E70.

in this paper, a new enhanced version of the particle swarm optimization (pso) is presented. an important modification is made by adding probabilistic functions into pso, and it is named probabilistic particle swarm optimization (ppso). since the variation of the velocity of particles in pso constitutes its search engine, it should provide two phases of optimization process which are: explorati...

Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Gué...

The present research work outlines the main ideas behind statistical regression by a 2-independent-variates and 1-dependent-variate model based on the invariance of measures in probabilistic spaces. The principle of probabilistic measure invariance, applied under the assumption that the model be isotonic, leads to a system of differential equations. Such differential system is reformulated in t...

Starting with a result on the nonexistence of the solution bounded between zero and one to a KPP-type equation, we explore the connection between these type of semilinear equations and probabilistic objects. We describe some methods where PDE techniques help in investigating properties of branching diffusions and superdiffusions as well as probabilistic approaches where these processes are expl...

In this paper, we extend Nilsson’s probabilistic logic [1] to allow that each sentence S has three sets of possible worlds. We adopt the ideas of consistency and possible worlds introduced by Nilsson in [1], but propose a new method called linear equation method to deal with the problems of probabilistic inference, the results of our method is consistent with those of Yao’s interval-set model m...

Two-frequency Wigner distribution is introduced to capture the asymptotic behaviour of the space–frequency correlation of paraxial waves in the radiative transfer limits. The scaling limits give rises to deterministic transport-like equations. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker–Planck-...

This paper analyzes indicative and counterfactual conditionals that have in their consequents probability operators: probable, likely, more likely than not, 50% chance and so on. I provide and motivate a unified compositional semantics for both kinds of probabilistic conditionals using a Kratzerian syntax for conditionals and a representation of information based on Causal Bayes Nets. On this a...