A stochastic control problem
Date
2004-11-23
Authors
Margulies, William
Zes, Dean
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
In this paper, we study a specific stochastic differential equation depending on a parameter and obtain a representation of its probability density function in terms of Jacobi Functions. The equation arose in a control problem with a quadratic performance criteria. The quadratic performance is used to eliminate the control in the standard Hamilton-Jacobi variational technique. The resulting stochastic differential equation has a noise amplitude which complicates the solution. We then solve Kolmogorov's partial differential equation for the probability density function by using Jacobi Functions. A particular value of the parameter makes the solution a Martingale and in this case we prove that the solution goes to zero almost surely as time tends to infinity.
Description
Keywords
Stochastic differential equations, Control problems, Jacobi functions
Citation
Margulies, W., & Zes, D. (2004). A stochastic control problem. <i>Electronic Journal of Differential Equations, 2004</i>(135), pp. 1-10.
Rights
Attribution 4.0 International