000			02213 a2200277 4500
003			OSt
005			20250113145243.0
008			250110b xxu||||| |||| 00| 0 eng d
020			_a9783030412906
040			_cIIT Kanpur
041			_aeng
082			_a519.22 _bK959a
100			_aKulinich, Grigorij
245			_aAsymptotic analysis of unstable solutions of stochastic differential equations _cGrigorij Kulinich, Svitlana Kushnirenko and Yuliya Mishura
260			_bSpringer _c2020 _aSwitzerland
300			_axv, 240p
440			_aBocconi and Springer series : mathematics, statistics, finance and economics
490			_a / edited by Beatrice Acciaio ...[et al.] _v; v.9
520			_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.
650			_aDifferential calculus and equations
650			_aMathematics functional analysis
650			_aStochastic differential equations
700			_aKushnirenko, Svitlana
700			_aMishura, Yuliya
942			_cBK
999			_c567325 _d567325