Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem
[EN] A computational approach to approximate the probability density function of random differential equations is based on transformation of random variables and finite difference schemes. The theoretical analysis of this computational method has not been performed in the extant literature. In this...
| Authors: | ; ; ; |
|---|---|
| Format: | Article |
| Publication date: | 2020 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/161848 |
| Online Access: | https://riunet.upv.es/handle/10251/161848 |
| Access Level: | Open access |
| Keyword: | Random diffusion-reaction Poisson-type problem Finite difference scheme Probability density function Numerical methods MATEMATICA APLICADA |
| _version_ | 1878734850285895680 |
|---|---|
| author | Calatayud, J. |
| author2 | Díaz, J.A. Jornet, M. Cortés, J.-C.|||0000-0002-6528-2155 |
| author2_role | author author author |
| author_browse | Calatayud, J. Cortés, J.-C.|||0000-0002-6528-2155 Díaz, J.A. Jornet, M. |
| author_facet | Calatayud, J. Díaz, J.A. Jornet, M. Cortés, J.-C.|||0000-0002-6528-2155 |
| author_role | author |
| collection | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| description | [EN] A computational approach to approximate the probability density function of random differential equations is based on transformation of random variables and finite difference schemes. The theoretical analysis of this computational method has not been performed in the extant literature. In this paper, we deal with a particular random differential equation: a random diffusion-reaction Poisson-type problem of the form , , with boundary conditions , . Here, alpha, A and B are random variables and is a stochastic process. The term is a stochastic process that solves the random problem in the sample path sense. Via a finite difference scheme, we approximate with a sequence of stochastic processes in both the almost sure and senses. This allows us to find mild conditions under which the probability density function of can be approximated. Illustrative examples are included. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_711b2cdbdfb42e0cfd3b1994e9dc1aa5 |
| institution | Universitat Politècnica de València (UPV) |
| instname_str | Universitat Politècnica de València (UPV) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:riunet.upv.es:10251/161848 |
| publishDate | 2020 |
| publishDateSort | 2020 |
| publisher | Taylor & Francis |
| publisherStr | Taylor & Francis |
| reponame_str | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| spelling | Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem Calatayud, J. Díaz, J.A. Jornet, M. Cortés, J.-C.|||0000-0002-6528-2155 Random diffusion-reaction Poisson-type problem Finite difference scheme Probability density function Numerical methods MATEMATICA APLICADA [EN] A computational approach to approximate the probability density function of random differential equations is based on transformation of random variables and finite difference schemes. The theoretical analysis of this computational method has not been performed in the extant literature. In this paper, we deal with a particular random differential equation: a random diffusion-reaction Poisson-type problem of the form , , with boundary conditions , . Here, alpha, A and B are random variables and is a stochastic process. The term is a stochastic process that solves the random problem in the sample path sense. Via a finite difference scheme, we approximate with a sequence of stochastic processes in both the almost sure and senses. This allows us to find mild conditions under which the probability density function of can be approximated. Illustrative examples are included. This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia. Taylor & Francis https://riunet.upv.es/handle/10251/161848 |
| spellingShingle | Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem Calatayud, J. Random diffusion-reaction Poisson-type problem Finite difference scheme Probability density function Numerical methods MATEMATICA APLICADA |
| title | Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem |
| title_full | Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem |
| title_fullStr | Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem |
| title_full_unstemmed | Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem |
| title_short | Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem |
| title_sort | Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem |
| topic | Random diffusion-reaction Poisson-type problem Finite difference scheme Probability density function Numerical methods MATEMATICA APLICADA |
| topic_facet | Random diffusion-reaction Poisson-type problem Finite difference scheme Probability density function Numerical methods MATEMATICA APLICADA |
| url | https://riunet.upv.es/handle/10251/161848 |