A probabilistic theory of random maps
We present a probabilistic theory of random maps with discrete time and continuous state. The forward and backward Kolmogorov equations as well as the FPK equation governing the evolution of the probability density function of the system are derived. The moment equations of arbitrary order are deriv...
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| Veröffentlicht in: | Communications in nonlinear science & numerical simulation 2005-10, Vol.10 (7), p.747-763 |
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| container_title | Communications in nonlinear science & numerical simulation |
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| creator | Elbeyli, O. Sun, J.Q. |
| description | We present a probabilistic theory of random maps with discrete time and continuous state. The forward and backward Kolmogorov equations as well as the FPK equation governing the evolution of the probability density function of the system are derived. The moment equations of arbitrary order are derived, and the reliability and first passage time problem are also studied. Examples are presented to demonstrate the application of the theoretical development. Numerical solutions including the time histories of moment evolution, steady state probability density function, reliability and first passage time probability density function for time discrete random maps are included. The present work compliments the existing theory of continuous time stochastic processes. |
| doi_str_mv | 10.1016/j.cnsns.2004.03.004 |
| format | Article |
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The present work compliments the existing theory of continuous time stochastic processes.</description><identifier>ISSN: 1007-5704</identifier><identifier>EISSN: 1878-7274</identifier><identifier>DOI: 10.1016/j.cnsns.2004.03.004</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Discrete stochastic systems ; First passage time probability ; FPK equation ; Moment equations ; Nonlinear PDEs ; Random maps ; Reliability</subject><ispartof>Communications in nonlinear science & numerical simulation, 2005-10, Vol.10 (7), p.747-763</ispartof><rights>2004 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c249t-23ccb782a3a3c1292eb3bf7203c91c0302d68a0cad3a0523583b992a0601c7663</citedby><cites>FETCH-LOGICAL-c249t-23ccb782a3a3c1292eb3bf7203c91c0302d68a0cad3a0523583b992a0601c7663</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cnsns.2004.03.004$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Elbeyli, O.</creatorcontrib><creatorcontrib>Sun, J.Q.</creatorcontrib><title>A probabilistic theory of random maps</title><title>Communications in nonlinear science & numerical simulation</title><description>We present a probabilistic theory of random maps with discrete time and continuous state. 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| ispartof | Communications in nonlinear science & numerical simulation, 2005-10, Vol.10 (7), p.747-763 |
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| subjects | Discrete stochastic systems First passage time probability FPK equation Moment equations Nonlinear PDEs Random maps Reliability |
| title | A probabilistic theory of random maps |
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