Margulies, WilliamZes, Dean2021-05-142021-05-142004-11-23Margulies, W., & Zes, D. (2004). A stochastic control problem. <i>Electronic Journal of Differential Equations, 2004</i>(135), pp. 1-10.1072-6691https://hdl.handle.net/10877/13556In 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.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalStochastic differential equationsControl problemsJacobi functionsArticle