04770nam 2200637Ia 450 991013946750332120170810183227.01-282-16484-897866121648420-470-61092-10-470-39351-3(CKB)2550000000006382(EBL)479825(OCoLC)521032017(SSID)ssj0000336195(PQKBManifestationID)11285764(PQKBTitleCode)TC0000336195(PQKBWorkID)10281829(PQKB)11447734(MiAaPQ)EBC479825(PPN)250684411(EXLCZ)99255000000000638220070305d2008 uy 0engur|n|---|||||txtccrContinuous semi-Markov processes[electronic resource] /Boris HarlamovLondon ISTE ;Hoboken, NJ Wiley20081 online resource (377 p.)ISTE ;v.8Description based upon print version of record.1-84821-005-1 Includes bibliographical references and index.Continuous Semi-Markov Processes; Contents; Introduction; Chapter 1. Stepped Semi-Markov Processes; 1.1. Random sequence; 1.2. Markov chain; 1.3. Two-dimensional Markov chain; 1.4. Semi-Markov process; 1.5. Stationary distributions; Chapter 2. Sequences of First Exit Times and Regeneration Times; 2.1. Basic maps; 2.2. Markov times; 2.3. Deducing sequences; 2.4. Correct exit and continuity; 2.5. Time of regeneration; Chapter 3. General Semi-Markov Processes; 3.1. Definition of a semi-Markov process; 3.2. Transition function of a SM process; 3.3. Operators and SM walk3.4. Operators and SM process3.5. Criterion of Markov property for SM processes; 3.6. Intervals of constancy; Chapter 4. Construction of Semi-Markov Processes using Semi-Markov Transition Functions; 4.1. Realization of an in nite system of pairs; 4.2. Extension of a measure; 4.3. Construction of a measure; 4.4. Construction of a projective system of measures; 4.5. Semi-Markov processes; Chapter 5. Semi-Markov Processes of Diffusion Type; 5.1. One-dimensional semi-Markov processes of diffusion type; 5.1.1. Differential equation; 5.1.2. Construction SM process5.1.3. Some properties of the process5.2. Multi-dimensional processes of diffusion type; 5.2.1. Differential equations of elliptic type; 5.2.2. Neighborhood of arbitrary form; 5.2.3. Neighborhood of spherical form; 5.2.4. Characteristic operator; Chapter 6. Time Change and Semi-Markov Processes; 6.1. Time change and trajectories; 6.2. Intrinsic time and traces; 6.3. Canonical time change; 6.4. Coordination of function and time change; 6.5. Random time changes; 6.6. Additive functionals; 6.7. Distribution of a time run along the trace; 6.8. Random curvilinear integrals6.9. Characteristic operator and integral6.10. Stochastic integral; 6.10.1. Semi-martingale and martingale; 6.10.2. Stochastic integral; 6.10.3. Ito-Dynkin's formula; Chapter 7. Limit Theorems for Semi-Markov Processes; 7.1. Weak compactness and weak convergence; 7.2. Weak convergence of semi-Markov processes; Chapter 8. Representation of a Semi-Markov Process as a Transformed Markov Process; 8.1. Construction by operator; 8.2. Comparison of processes; 8.3. Construction by parameters of Lévy formula; 8.4. Stationary distribution; Chapter 9. Semi-Markov Model of Chromatography9.1. Chromatography9.2. Model of liquid column chromatography; 9.3. Some monotone Semi-Markov processes; 9.4. Transfer with diffusion; 9.5. Transfer with final absorption; Bibliography; IndexThis title considers the special of random processes known as semi-Markov processes. These possess the Markov property with respect to any intrinsic Markov time such as the first exit time from an open set or a finite iteration of these times.The class of semi-Markov processes includes strong Markov processes, Lévy and Smith stepped semi-Markov processes, and some other subclasses. Extensive coverage is devoted to non-Markovian semi-Markov processes with continuous trajectories and, in particular, to semi-Markov diffusion processes. Readers looking to enrich their knowledge on Markov proceISTEMarkov processesRenewal theoryMarkov processes.Renewal theory.519.2/33519.233Harlamov Boris870795MiAaPQMiAaPQMiAaPQBOOK9910139467503321Continuous semi-Markov processes1954882UNINA