LEADER 02905nam 22005412 450 001 9910159458503321 005 20170308135427.0 010 $a1-316-86682-3 010 $a1-316-86790-0 010 $a1-316-86808-7 010 $a1-139-20846-2 010 $a1-316-86826-5 010 $a1-316-86844-3 010 $a1-316-86898-2 035 $a(CKB)3710000001008904 035 $a(UkCbUP)CR9781139208468 035 $a(MiAaPQ)EBC4784002 035 $a(PPN)261296752 035 $a(EXLCZ)993710000001008904 100 $a20111205d2017|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNon-homogeneous random walks $eLyapunov function methods for near-critical stochastic systems /$fMikhail Menshikov, University of Durham, Serguei Popov, Universidade Estadual de Campinas, Brazil, Andrew Wade, University of Durham$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2017. 215 $a1 online resource (xviii, 363 pages) $cdigital, PDF file(s) 225 1 $aCambridge tracts in mathematics ;$v209 300 $aTitle from publisher's bibliographic system (viewed on 28 Feb 2017). 311 $a1-107-02669-5 311 $a1-316-86880-X 330 $aStochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems. 410 0$aCambridge tracts in mathematics ;$v209. 606 $aRandom walks (Mathematics) 606 $aStochastic processes 615 0$aRandom walks (Mathematics) 615 0$aStochastic processes. 676 $a519.2/82 700 $aMen?shikov$b M. V$g(Mikhail Vasil?evich),$0850776 702 $aPopov$b Serguei$f1972- 702 $aWade$b Andrew$g(Andrew R.),$f1981- 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910159458503321 996 $aNon-homogeneous random walks$91899644 997 $aUNINA LEADER 01901nam 2200433z- 450 001 9910557496603321 005 20211118 035 $a(CKB)5400000000042865 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/73220 035 $a(oapen)doab73220 035 $a(EXLCZ)995400000000042865 100 $a20202111d2019 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aCognitive Enhancement in Psychiatric Disorders 210 $cFrontiers Media SA$d2019 215 $a1 online resource (261 p.) 311 08$a2-88963-055-2 330 $aThis eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact 606 $aMedicine and Nursing$2bicssc 606 $aPsychiatry$2bicssc 610 $aAssessment 610 $aBiomarkers 610 $aCognition 610 $aFunctional outcomes 610 $aTherapeutics 615 7$aMedicine and Nursing 615 7$aPsychiatry 700 $aSumiyoshi$b Tomiki$4edt$01322353 702 $aHashimoto$b Kenji$4edt 702 $aSumiyoshi$b Tomiki$4oth 702 $aHashimoto$b Kenji$4oth 906 $aBOOK 912 $a9910557496603321 996 $aCognitive Enhancement in Psychiatric Disorders$93034900 997 $aUNINA