We derive Edgeworth-type expansions for Skorohod and Itô integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain Stein approximation bounds for stochastic integrals, which apply to SDE solutions and to multiple stochastic integrals.

This paper describes some of the results in [5] for a stochastic calculus for a fractional Brownian motion with the Hurst parameter in the interval (1/2, 1). Two stochastic integrals are defined with explicit expressions for their first two moments. Multiple and iterated integrals of a fractional Browinian motion are defined and various properties of these integrals are given. A square integrab...

We show that iterated stochastic integrals can be described equivalently either by the conventional forward adapted, or by backward adapted quantum stochastic calculus. By using this equivalence we establish two properties of triangular (causal) and rectangular double quantum stochastic product integrals, namely a necessary and su¢ cient condition for their unitarity, and the coboundary relatio...

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...

The subject of this paper is stochastic integration in the context of free probability. Noncommutative stochastic processes with freely independent increments, especially the free Brownian motion, have been investigated in a number of sources, see [BS98], [Ans00] and their references. In the latter paper, we started the analysis of such processes, which we also call free stochastic measures, us...