LEADER 03011nam 2200529 450 001 9910467623703321 005 20200923020339.0 010 $a3-11-045871-3 024 7 $a10.1515/9783110458930 035 $a(CKB)4100000001044529 035 $a(MiAaPQ)EBC5158156 035 $a(DE-B1597)461078 035 $a(OCoLC)1024011121 035 $a(DE-B1597)9783110458930 035 $a(Au-PeEL)EBL5158156 035 $a(CaPaEBR)ebr11473972 035 $a(OCoLC)1013828739 035 $a(EXLCZ)994100000001044529 100 $a20171222h20182018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aErgodic behavior of Markov processes $ewith applications to limit theorems /$fAlexei Kulik 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2018. 210 4$dİ2018 215 $a1 online resource (268 pages) 225 1 $aDe Gruyter Studies in Mathematics,$x01790986 ;$vVolume 67 311 $a3-11-045870-5 311 $a3-11-045893-4 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tPreface -- $tContents -- $tIntroduction -- $tPart I: Ergodic Rates for Markov Chains and Processes -- $t1. Markov Chains with Discrete State Spaces -- $t2. General Markov Chains: Ergodicity in Total Variation -- $t3. Markov Processes with Continuous Time -- $t4. WeakErgodicRates -- $tPart II: Limit Theorems -- $t5. The Law of Large Numbers and the Central Limit Theorem -- $t6. Functional Limit Theorems -- $tBibliography -- $tIndex 330 $aThe general topic of this book is the ergodic behavior of Markov processes. A detailed introduction to methods for proving ergodicity and upper bounds for ergodic rates is presented in the first part of the book, with the focus put on weak ergodic rates, typical for Markov systems with complicated structure. The second part is devoted to the application of these methods to limit theorems for functionals of Markov processes. The book is aimed at a wide audience with a background in probability and measure theory. Some knowledge of stochastic processes and stochastic differential equations helps in a deeper understanding of specific examples. Contents?Part I: Ergodic Rates for Markov Chains and ProcessesMarkov Chains with Discrete State SpacesGeneral Markov Chains: Ergodicity in Total VariationMarkovProcesseswithContinuousTimeWeak Ergodic Rates Part II: Limit TheoremsThe Law of Large Numbers and the Central Limit TheoremFunctional Limit Theorems 410 0$aDe Gruyter studies in mathematics ;$vVolume 67. 606 $aMarkov processes$vTextbooks 608 $aElectronic books. 615 0$aMarkov processes 676 $a519.233 700 $aKulik$b Alexei$01048232 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910467623703321 996 $aErgodic behavior of Markov processes$92476395 997 $aUNINA