%0 Journal Article %T A stochastic control problem %A William Margulies %A Dean Zes %J Electronic Journal of Differential Equations %D 2004 %I Texas State University %X 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. %K Stochastic differential equations %K control problems %K Jacobi functions. %U http://ejde.math.txstate.edu/Volumes/2004/135/abstr.html