Stochastic process measurability conditions

Approximations of Stochastic Optimization Problems Subject to Measurability Constraints

Motivated by the numerical resolution of stochastic optimization problems subject to measurability constraints, we focus upon the issue of how to discretize the components arising in the problem formulation. By means of a counterexample based on Monte Carlo approximation, we emphasize the importance of independent discretization of, on the one side, the random variable modelling uncertainties (...

Measurability and Continuity Conditions for Nonlinear Evolutionary Processes

This paper generalizes to nonlinear evolutionary processes on a metric space the well-known results connecting measurability and continuity properties with respect to time of linear semigroups of continuous operators on a Banach space.

Stochastic Bandwidth Packing Process: Stability Conditions via Lyapunov Function Technique

We consider the following stochastic bandwidth packing process: the requests for communication bandwidth of different sizes arrive at times t = 0, 1, 2, . . . and are allocated to a communication link using “largest first” rule. Each request takes a unit time to complete. The unallocated requests form queues. Coffman and Stolyar [6] introduced this system and posed the following question: under...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Stochastic Process

Recent research has investigated ways in which general probability distributions may be incorporated into stochastic process algebra. These proposals allow the arbitrary use of such distributions, improving expressibility, but in general this makes performance evaluation diicult. Typically, simulation techniques must be employed. We attack the goal of general probability distributions from the ...