In this paper we introduce and study the notion of safety control of stochastic discrete event systems (DESs), modeled as controlled Markov chains. For non-stochastic DESs, modeled by state machines or automata, safety is specified as a set of forbidden states, or equivalently by a binary valued vector that imposes an upper bound on the set of states permitted to be visited. We generalize this ...

Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains ...

We derive the chaotic expansion of the product of nthand ®rst-order multiple stochastic integrals with respect to certain normal martingales. This is done by application of the classical and quantum product formulae for multiple stochastic integrals. Our approach extends existing results on chaotic calculus for normal martingales and exhibits properties, relative to multiple stochastic integral...

In contrast to construction of integrals as limits of Riemann sums, the Gelfand-Pettis characterization is a property no reasonable notion of integral would lack. Since this property is an irreducible minimum, this definition of integral is called a weak integral. Uniqueness of the integral is immediate when the dual V ∗ separates points, meaning that for v 6 v′ in V there is λ ∈ V ∗ with λv 6=...

In this paper, using fuzzy complex valued functions and fuzzy complex valued fuzzy measures ([11]) and interval-valued Choquet integrals ([2-6]), we define Choquet integral with respect to a fuzzy complex valued fuzzy measure of a fuzzy complex valued function and investigate some basic properties of them.

Stochastic integration rules are derived for innnite integration intervals, generalizing rules developed by Siegel and O'Brien (1985) for nite intervals. Then random orthogonal transformations of rules for integrals over the surface of the unit m-sphere are used to produce stochastic rules for these integrals. The two types of rules are combined to produce stochastic rules for multidimensional ...