Analytic and numerical solutions of a Riccati differential equation with random coefficients
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 composi...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2013-02, Vol.239, p.208-219 |
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| container_title | Journal of computational and applied mathematics |
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| creator | Licea, J.A. Villafuerte, L. Chen-Charpentier, B.M. |
| description | 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 C1 function and a stochastic process belonging to the Banach space Lp, 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. |
| doi_str_mv | 10.1016/j.cam.2012.09.040 |
| format | Article |
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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 C1 function and a stochastic process belonging to the Banach space Lp, 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.</description><subject>Computer simulation</subject><subject>Differential equations</subject><subject>Exact solutions</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mean square calculus</subject><subject>Monte Carlo method</subject><subject>Monte Carlo methods</subject><subject>Polynomial chaos</subject><subject>Random differential equations</subject><subject>Riccati equation</subject><subject>Stochastic processes</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLxDAUhYMoOD5-gLss3bTe2zZNgysRXzAgiO6EkElvMEPbjEmr-O9tGdeuzuY7B87H2AVCjoD11Ta3ps8LwCIHlUMFB2yFjVQZStkcshWUUmZQFfKYnaS0BYBaYbVi7zeD6X5Gb7kZWj5MPUVvTcdT6KbRhyHx4LjhL95aM3reeuco0jD6maHPySwM__bjB4_zQOi5DeSct35m0hk7cqZLdP6Xp-zt_u719jFbPz883d6sM1vKcsxsVbQOaomlaAS1UroK0aGsSbiNFA5KQdBUSrhGbUAZo5TAxhRtVVgnBJan7HK_u4vhc6I06t4nS11nBgpT0rhsNzWW9YziHrUxpBTJ6V30vYk_GkEvJvVWzyb1YlKD0rPJuXO979D84ctT1Gn5Z6n1keyo2-D_af8Ce_x8IA</recordid><startdate>20130201</startdate><enddate>20130201</enddate><creator>Licea, J.A.</creator><creator>Villafuerte, L.</creator><creator>Chen-Charpentier, B.M.</creator><general>Elsevier B.V</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20130201</creationdate><title>Analytic and numerical solutions of a Riccati differential equation with random coefficients</title><author>Licea, J.A. ; Villafuerte, L. ; Chen-Charpentier, B.M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c373t-c42df06713585ed77f411f176e5fb75f035e08495f89b09aa99518a2d42cf5513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Computer simulation</topic><topic>Differential equations</topic><topic>Exact solutions</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mean square calculus</topic><topic>Monte Carlo method</topic><topic>Monte Carlo methods</topic><topic>Polynomial chaos</topic><topic>Random differential equations</topic><topic>Riccati equation</topic><topic>Stochastic processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Licea, J.A.</creatorcontrib><creatorcontrib>Villafuerte, L.</creatorcontrib><creatorcontrib>Chen-Charpentier, B.M.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Licea, J.A.</au><au>Villafuerte, L.</au><au>Chen-Charpentier, B.M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analytic and numerical solutions of a Riccati differential equation with random coefficients</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2013-02-01</date><risdate>2013</risdate><volume>239</volume><spage>208</spage><epage>219</epage><pages>208-219</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><abstract>In this paper an analytic mean square solution of a Riccati equation with randomness in the coefficients and initial condition is given. 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| ispartof | Journal of computational and applied mathematics, 2013-02, Vol.239, p.208-219 |
| issn | 0377-0427 1879-1778 |
| language | eng |
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| source | Elsevier ScienceDirect Journals Complete; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Computer simulation Differential equations Exact solutions Mathematical analysis Mathematical models Mean square calculus Monte Carlo method Monte Carlo methods Polynomial chaos Random differential equations Riccati equation Stochastic processes |
| title | Analytic and numerical solutions of a Riccati differential equation with random coefficients |
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