A stochastic control problem
| dc.contributor.author | Margulies, William | |
| dc.contributor.author | Zes, Dean | |
| dc.date.accessioned | 2021-05-14T20:31:06Z | |
| dc.date.available | 2021-05-14T20:31:06Z | |
| dc.date.issued | 2004-11-23 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Margulies, W., & Zes, D. (2004). A stochastic control problem. <i>Electronic Journal of Differential Equations, 2004</i>(135), pp. 1-10. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13556 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2004, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Stochastic differential equations | |
| dc.subject | Control problems | |
| dc.subject | Jacobi functions | |
| dc.title | A stochastic control problem | |
| dc.type | Article |