The problem of global solution of Fredholm integral equations is studied. This means that one seeks to approximate the full solution function (as opposed to the local problem, where only the value of the solution in a single point or a functional of the solution is sought). The Monte Carlo complexity is analyzed, i. e. the complexity of stochastic solution of this problem. The framework for thi...

in this paper we use a class of stochastic functional kolmogorov-type model with jumps to describe the evolutions of population dynamics. by constructing a special lyapunov function, we show that the stochastic functional differential equation associated with our model admits a unique global solution in the positive orthant, and, by the exponential martingale inequality with jumps, we dis...

Burgers’ equation with stochastic initial and boundary conditions is investigated by a polynomial chaos expansion approach where the solution is represented as a series of stochastic, orthogonal polynomials. The analysis of wellposedness for the stochastic Burgers’ equation follows the pattern of that of the deterministic Burgers’ equation. We use dissipation and spatial derivative operators sa...

Planning horizon is a key issue in production planning. Different from previous approaches based on Markov Decision Processes, we study the planning horizon of capacity planning problems within the framework of stochastic programming. We first consider an infinite horizon stochastic capacity planning model involving a single resource, linear cost structure, and discrete distributions for genera...