Towards a Theory of Stochastic Hybrid Systems
In this paper, we present a scheme of stochastic hybrid system which introduces randomness to the deterministic framework of the traditional hybrid systems by allowing the flow inside each invariant set of the discrete state variables to be governed by stochastic differential equation (SDE) rather t...
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creator | Hu, Jianghai Lygeros, John Sastry, Shankar |
description | In this paper, we present a scheme of stochastic hybrid system which introduces randomness to the deterministic framework of the traditional hybrid systems by allowing the flow inside each invariant set of the discrete state variables to be governed by stochastic differential equation (SDE) rather than the deterministic ones. The notion of embedded Markov chains is proposed for such systems and some illustrative example from high way model is presented. As an important application, these ideas are then applied to the state space discretization of one dimensional SDE to obtain the natural discretized stochastic hybrid system together with its embedded MC. The invariant distribution and exit probability from interval of the MC are studied and it is shown that they converge to their counterparts for the solution process of the original SDE as the discretization step goes to zero. As a result, the discretized stochastic hybrid system provides a useful tool for studying various sample path properties of the SDE. |
doi_str_mv | 10.1007/3-540-46430-1_16 |
format | Book Chapter |
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The notion of embedded Markov chains is proposed for such systems and some illustrative example from high way model is presented. As an important application, these ideas are then applied to the state space discretization of one dimensional SDE to obtain the natural discretized stochastic hybrid system together with its embedded MC. The invariant distribution and exit probability from interval of the MC are studied and it is shown that they converge to their counterparts for the solution process of the original SDE as the discretization step goes to zero. As a result, the discretized stochastic hybrid system provides a useful tool for studying various sample path properties of the SDE.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540672593</identifier><identifier>ISBN: 3540672591</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540464303</identifier><identifier>EISBN: 3540464301</identifier><identifier>DOI: 10.1007/3-540-46430-1_16</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied sciences ; Computer science; control theory; systems ; Control system analysis ; Control theory. 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The notion of embedded Markov chains is proposed for such systems and some illustrative example from high way model is presented. As an important application, these ideas are then applied to the state space discretization of one dimensional SDE to obtain the natural discretized stochastic hybrid system together with its embedded MC. The invariant distribution and exit probability from interval of the MC are studied and it is shown that they converge to their counterparts for the solution process of the original SDE as the discretization step goes to zero. As a result, the discretized stochastic hybrid system provides a useful tool for studying various sample path properties of the SDE.</description><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Control system analysis</subject><subject>Control theory. Systems</subject><subject>Embed Markov Chain</subject><subject>Exact sciences and technology</subject><subject>Markov Chain</subject><subject>Positive Recurrence</subject><subject>Probability Transition Matrix</subject><subject>State Space Discretization</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540672593</isbn><isbn>3540672591</isbn><isbn>9783540464303</isbn><isbn>3540464301</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2000</creationdate><recordtype>book_chapter</recordtype><recordid>eNo9kL1PwzAUxM2XRFW6M2ZgdXnPzx_JiCqgSJUYWmbLdlwaaJvKjoTy35O2iFtOujvd8GPsHmGKAOaRuJLApZYEHC3qCzapTElDeMroko1QI3IiWV39d9oIVdE1GwGB4JWRdMsmOX_BIBJUaj1ifNX-uFTnwhWrTWxTX7TrYtm1YeNy14Ri3vvU1MWyz13c5Tt2s3bbHCd_PmYfL8-r2Zwv3l_fZk8LHghFx0sjYwAFwjgVvVJYQwkIWLmg6tJgCCQUKa2cL0Er40WtCVTw2sdYe0lj9nD-Pbgc3Had3D402R5Ss3Opt4jGyAqG2fQ8y0Oz_4zJ-rb9zhbBHrFZsgMFe0Jkj9joF3GlWC0</recordid><startdate>2000</startdate><enddate>2000</enddate><creator>Hu, Jianghai</creator><creator>Lygeros, John</creator><creator>Sastry, Shankar</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>IQODW</scope></search><sort><creationdate>2000</creationdate><title>Towards a Theory of Stochastic Hybrid Systems</title><author>Hu, Jianghai ; Lygeros, John ; Sastry, Shankar</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c312t-874ec05027a5eb551d0801019ac5d871cc3253565ab80657b2d6305cb6beedb43</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2000</creationdate><topic>Applied sciences</topic><topic>Computer science; control theory; systems</topic><topic>Control system analysis</topic><topic>Control theory. Systems</topic><topic>Embed Markov Chain</topic><topic>Exact sciences and technology</topic><topic>Markov Chain</topic><topic>Positive Recurrence</topic><topic>Probability Transition Matrix</topic><topic>State Space Discretization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hu, Jianghai</creatorcontrib><creatorcontrib>Lygeros, John</creatorcontrib><creatorcontrib>Sastry, Shankar</creatorcontrib><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hu, Jianghai</au><au>Lygeros, John</au><au>Sastry, Shankar</au><au>Krogh, Bruce H.</au><au>Lynch, Nancy</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>Towards a Theory of Stochastic Hybrid Systems</atitle><btitle>Hybrid Systems: Computation and Control</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>2000</date><risdate>2000</risdate><spage>160</spage><epage>173</epage><pages>160-173</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540672593</isbn><isbn>3540672591</isbn><eisbn>9783540464303</eisbn><eisbn>3540464301</eisbn><abstract>In this paper, we present a scheme of stochastic hybrid system which introduces randomness to the deterministic framework of the traditional hybrid systems by allowing the flow inside each invariant set of the discrete state variables to be governed by stochastic differential equation (SDE) rather than the deterministic ones. 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language | eng |
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source | Springer Books |
subjects | Applied sciences Computer science control theory systems Control system analysis Control theory. Systems Embed Markov Chain Exact sciences and technology Markov Chain Positive Recurrence Probability Transition Matrix State Space Discretization |
title | Towards a Theory of Stochastic Hybrid Systems |
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