LEADER 04770nam 2200637Ia 450 001 9910139467503321 005 20170810183227.0 010 $a1-282-16484-8 010 $a9786612164842 010 $a0-470-61092-1 010 $a0-470-39351-3 035 $a(CKB)2550000000006382 035 $a(EBL)479825 035 $a(OCoLC)521032017 035 $a(SSID)ssj0000336195 035 $a(PQKBManifestationID)11285764 035 $a(PQKBTitleCode)TC0000336195 035 $a(PQKBWorkID)10281829 035 $a(PQKB)11447734 035 $a(MiAaPQ)EBC479825 035 $a(PPN)250684411 035 $a(EXLCZ)992550000000006382 100 $a20070305d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aContinuous semi-Markov processes$b[electronic resource] /$fBoris Harlamov 210 $aLondon $cISTE ;$aHoboken, NJ $cWiley$d2008 215 $a1 online resource (377 p.) 225 1 $aISTE ;$vv.8 300 $aDescription based upon print version of record. 311 $a1-84821-005-1 320 $aIncludes bibliographical references and index. 327 $aContinuous 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 walk 327 $a3.4. 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 process 327 $a5.1.3. 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 integrals 327 $a6.9. 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 Le?vy formula; 8.4. Stationary distribution; Chapter 9. Semi-Markov Model of Chromatography 327 $a9.1. 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; Index 330 $aThis title considers the special of random processes known as semi-Markov processes. These possess the Markov property with respect to any intrinsic Markov time such as the first exit time from an open set or a finite iteration of these times.The class of semi-Markov processes includes strong Markov processes, Le?vy and Smith stepped semi-Markov processes, and some other subclasses. Extensive coverage is devoted to non-Markovian semi-Markov processes with continuous trajectories and, in particular, to semi-Markov diffusion processes. Readers looking to enrich their knowledge on Markov proce 410 0$aISTE 606 $aMarkov processes 606 $aRenewal theory 615 0$aMarkov processes. 615 0$aRenewal theory. 676 $a519.2/33 676 $a519.233 700 $aHarlamov$b Boris$0870795 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139467503321 996 $aContinuous semi-Markov processes$91954882 997 $aUNINA