Analytic and numerical solutions of a Riccati differential equation with random coefficients

Authors:
J. A. Licea;L. Villafuerte;B. M. Chen-Charpentier
Affiliations:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA;Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA and CEFyMAP, Universidad Autónoma de Chiapas, Calle 4a. Ote. Nte. No. 1428, Tuxtla Gutiérrez, Chiapa ...;Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

In this paper an analytic mean square solution of a Riccati equation with randomness in the coefficients and initial condition is given. This analytic solution can be expressed in an explicit form by using a general theorem for the chain rule for stochastic processes that can be written as a composition of a C^1 function and a stochastic process belonging to the Banach space L"p, p=1. Moreover, the exact mean and variance functions of the Riccati equation are computed and they are compared to those obtained by Monte Carlo, Differential Transform and Generalized Chaos Polynomial methods. Advantages and disadvantages of these methods are discussed for this equation.