LEADER 03015nam 22005535 450 001 9910153303503321 005 20251113210922.0 010 $a3-319-46979-7 024 7 $a10.1007/978-3-319-46979-9 035 $a(CKB)3710000000961030 035 $a(DE-He213)978-3-319-46979-9 035 $a(MiAaPQ)EBC4746682 035 $a(PPN)197138918 035 $a(EXLCZ)993710000000961030 100 $a20161121d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAsymptotic Analysis for Functional Stochastic Differential Equations /$fby Jianhai Bao, George Yin, Chenggui Yuan 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XVI, 151 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8201 311 08$a3-319-46978-9 320 $aIncludes bibliographical references and index. 327 $aPreface and Introduction -- Notation -- Ergodicity for Functional Stochastic Equations under Dissipativity -- Ergodicity for Functional Stochastic Equations without Dissipativity -- Convergence Rate of Euler-Maruyama Scheme for FSDEs -- Large Deviations for FSDEs -- Stochastic Interest Rate Models with Memory: Long-Term Behavior -- Existence and Uniqueness -- Markov Property and Variation of Constants Formulas. 330 $aThis brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity. This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes. 410 0$aSpringerBriefs in Mathematics,$x2191-8201 606 $aProbabilities 606 $aDifferential equations 606 $aProbability Theory 606 $aDifferential Equations 615 0$aProbabilities. 615 0$aDifferential equations. 615 14$aProbability Theory. 615 24$aDifferential Equations. 676 $a519.2 700 $aBao$b Jianhai$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755838 702 $aYin$b George$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aYuan$b Chenggui$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910153303503321 996 $aAsymptotic Analysis for Functional Stochastic Differential Equations$92044164 997 $aUNINA