We present here a method for the study of stochastic neurodynamics in the framework of the "Neural Network Master Equation" proposed by Cowan. We consider a model neural network composed of two{state neurons subject to simple stochastic kinetics. We introduce a method based on a spin choerent state path integral to compute the moment generating function of such a network. A formal construction ...

In this paper we propose a new approach to fuzzy stochastic integrals of Itô and Aumann type. Then a fuzzy equation with fuzzy stochastic integrals is investigated. The existence and uniqueness of solution is proven. Some typical properties of the solution are also obtained. Similar results to set-valued stochastic integral equations are stated.

Many microeconomic and engineering problems can be formulated as stochastic optimization problems that are modelled by Itô evolution systems and by cost functionals expressed as stochastic integrals. Our paper studies some optimization problems constrained by stochastic evolution systems, giving original results on stochastic first integrals, adjoint stochastic processes and a version of simpli...

Schürmann's theory of quantum Lévy processes, and more generally the theory of quantum stochastic convolution cocycles, is extended to the topological context of compact quantum groups and operator space coalge-bras. Quantum stochastic convolution cocycles on a C *-hyperbialgebra, which are Markov-regular, completely positive and contractive, are shown to satisfy coalgebraic quantum stochastic ...

A method for forward and inverse integration of a class of population balance equations with a size-dependent growth rate is contributed in this article. A unique differential transformation of the independent time and internal coordinates is introduced, leading to straight line characteristics with constant values for the density function. The evolution of the density function is then given by...

Schürmann’s theory of quantum Lévy processes, and more generally the theory of quantum stochastic convolution cocycles, is extended to the topological context of compact quantum groups and operator space coalgebras. Quantum stochastic convolution cocycles on a C-hyperbialgebra, which are Markov-regular, completely positive and contractive, are shown to satisfy coalgebraic quantum stochastic dif...