Stochastic initial boundary value problems subject to distributed and boundary noise and their optimal control

Boundary value problems in stochastic optimal control of advertising

Temporal patterns for advertising include constant spending over time, decreasing spending over time and increasing spending over time. This research shows that all these spending patterns emerge at optimality for the same response function dynamics, due to differences in salvage value assumptions. I use these results to develop a methodology for determining the optimal planning horizon length ...

A White Noise Approach to Stochastic Neumann Boundary Value Problems

We illustrate the use of white noise analysis in the solution of stochastic partial diierential equations by solving explicitly the stochastic Neumann boundary value problem LU(x) ? c(x)U(x) = 0; x 2 D R d ; (x) rU(x) = ?W(x); x 2 @D where L is a uniformly elliptic linear partial diierential operator and W (x), x 2 R d , is d-parameter white noise. 1. Introduction Since the seminal book by Hida...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Solving Discrete Initial- and Boundary-Value Problems

Multivariate linear recurrences appear in such diverse elds of mathematics as combinatorics, probability theory, and numerical resolution of partial diierential equations. Whereas in the univariate case the solution of a constant-coeecient recurrence always has a rational generating function, this is no longer true in the multivariate case where this generating function can be non-rational, non...

Optimal Control of a Stochastic Heat Equation with Boundary-noise and Boundary-control

We are here concerned with an optimal control problem for a state equation of parabolic type on a bounded real interval, which for convenience we take equal to [0, π]. We stress the fact that we consider Neumann boundary conditions in which the derivative of the unknown is equal to the sum of the control and of a white noise in time, namely:  ∂y ∂s (s, ξ) = ∂2y ∂ξ2 (s, ξ) + f(s, y(s, ξ)...