Solving Riccati time-dependent models with random quadratic coefficient
This paper deals with the construction of approximate solutions of a random logistic differential equation whose nonlinear coefficient is assumed to be an analytic stochastic process and the initial condition is a random variable. Applying p-mean stochastic calculus, the nonlinear equation is transf...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/62893 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/62893 |
| Access Level: | acceso abierto |
| Palabra clave: | P-mean stochastic calculus Random logistic differential equation Random power series solution Analyticity Approximate solution Initial conditions Linear problems Monte Carlo Simulation Nonlinear coefficient Nonlinear problems Power series solutions Quadratic coefficients Stochastic calculus Stochastic process Time-dependent models Calculations Computer simulation Differential equations Differentiation (calculus) Monte Carlo methods Nonlinear equations Random processes Stochastic models Stochastic systems Random variables MATEMATICA APLICADA |
| Sumario: | This paper deals with the construction of approximate solutions of a random logistic differential equation whose nonlinear coefficient is assumed to be an analytic stochastic process and the initial condition is a random variable. Applying p-mean stochastic calculus, the nonlinear equation is transformed into a random linear equation whose coefficients keep analyticity. Next, an approximate solution of the nonlinear problem is constructed in terms of a random power series solution of the associate linear problem. Approximations of the average and variance of the solution are provided. The proposed technique is illustrated through an example where comparisons with respect to Monte Carlo simulations are shown. © 2011 Elsevier Ltd. All rights reserved. |
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