Probabilistic solution of the homogeneous Riccati differential equation: a case-study by using linearization and transformation techniques. (English) Zbl 1339.60068
Summary: This paper deals with the determination of the first probability density function of the solution stochastic process to the homogeneous Riccati differential equation taking advantage of both linearization and random variable transformation techniques. The study is split in all possible casuistries regarding the deterministic/random character of the involved input parameters. An illustrative example is provided for each one of the considered cases.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 34F05 | Ordinary differential equations and systems with randomness |
| 93E20 | Optimal stochastic control |
Keywords:
random Riccati differential equations; random variable transformation technique; first probability density functionReferences:
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