LEADER 04988nam 22007095 450 001 996418186803316 005 20200703145010.0 010 $a3-030-41291-1 024 7 $a10.1007/978-3-030-41291-3 035 $a(CKB)4920000000496071 035 $a(DE-He213)978-3-030-41291-3 035 $a(MiAaPQ)EBC6187801 035 $a(PPN)243762097 035 $a(EXLCZ)994920000000496071 100 $a20200429d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAsymptotic Analysis of Unstable Solutions of Stochastic Differential Equations$b[electronic resource] /$fby Grigorij Kulinich, Svitlana Kushnirenko, Yuliya Mishura 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XV, 240 p. 4 illus., 2 illus. in color.) 225 1 $aBocconi & Springer Series, Mathematics, Statistics, Finance and Economics,$x2039-1471 ;$v9 311 $a3-030-41290-3 327 $aIntroduction to Unstable Processes and Their Asymptotic Behavior -- Convergence of Unstable Solutions of SDEs to Homogeneous Markov Processes with Discontinuous Transition Density -- Asymptotic Analysis of Equations with Ergodic and Stochastically Unstable Solutions -- Asymptotic Behavior of Integral Functionals of Stochastically Unstable Solutions -- Asymptotic Behavior of Homogeneous Additive Functionals Defined on the Solutions of Itô SDEs with Non-regular Dependence on a Parameter -- Asymptotic Behavior of Homogeneous Additive Functionals of the Solutions to Inhomogeneous Itô SDEs with Non-regular Dependence on a Parameter -- A Selected Facts and Auxiliary Results -- References. 330 $aThis book is devoted to unstable solutions of stochastic differential equations (SDEs). Despite the huge interest in the theory of SDEs, this book is the first to present a systematic study of the instability and asymptotic behavior of the corresponding unstable stochastic systems. The limit theorems contained in the book are not merely of purely mathematical value; rather, they also have practical value. Instability or violations of stability are noted in many phenomena, and the authors attempt to apply mathematical and stochastic methods to deal with them. The main goals include exploration of Brownian motion in environments with anomalies and study of the motion of the Brownian particle in layered media. A fairly wide class of continuous Markov processes is obtained in the limit. It includes Markov processes with discontinuous transition densities, processes that are not solutions of any Itô's SDEs, and the Bessel diffusion process. The book is self-contained, with presentation of definitions and auxiliary results in an Appendix. It will be of value for specialists in stochastic analysis and SDEs, as well as for researchers in other fields who deal with unstable systems and practitioners who apply stochastic models to describe phenomena of instability. . 410 0$aBocconi & Springer Series, Mathematics, Statistics, Finance and Economics,$x2039-1471 ;$v9 606 $aProbabilities 606 $aDynamics 606 $aErgodic theory 606 $aDifferential equations 606 $aFunctional analysis 606 $aPartial differential equations 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aProbabilities. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aDifferential equations. 615 0$aFunctional analysis. 615 0$aPartial differential equations. 615 14$aProbability Theory and Stochastic Processes. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aOrdinary Differential Equations. 615 24$aFunctional Analysis. 615 24$aPartial Differential Equations. 676 $a519.2 700 $aKulinich$b Grigorij$4aut$4http://id.loc.gov/vocabulary/relators/aut$01015244 702 $aKushnirenko$b Svitlana$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMishura$b Yuliya$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418186803316 996 $aAsymptotic Analysis of Unstable Solutions of Stochastic Differential Equations$92369944 997 $aUNISA