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- W1530056693 abstract "In this paper, we study a specific stochastic dierential equation depending on a parameter and obtain a representation of its probability den- sity 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 dierential equation has a noise amplitude which complicates the solution. We then solve Kolmogorov's partial dieren- tial 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." @default.
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- W1530056693 date "2004-11-23" @default.
- W1530056693 modified "2023-09-27" @default.
- W1530056693 title "A stochastic control problem" @default.
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