105 records matched your query       

04743aam a2200373 i 4500
001 4F267466C38A11E7B100357297128E48
003 SILO
005 20171107010627
008 160815s2017    enka     b    001 0 eng  
010    $a 2016036262
020    $a 1107026695 (hardback : alk. paper)
020    $a 9781107026698 (hardback : alk. paper)
035    $a (OCoLC)956946977
040    $a DLC $b eng $e rda $c DLC $d OCLCF $d YDX $d BNG $d IPS $d U3G $d QCL $d FIE $d IWA $d SILO
042    $a pcc
100 1  $a Menʹshikov, M. V. $q (Mikhail Vasilʹevich), $e author.
245 10 $a Non-homogeneous random walks : $b Lyapunov function methods for near-critical stochastic systems / $c Mikhail Menshikov, University of Durham, Serguei Popov, Universidade Estadual de Campinas, Brazil, Andrew Wade, University of Durham.
264  1 $a Cambridge : $b Cambridge University Press, $c [2017]
300    $a xviii, 363 pages : $b illustrations ; $c 24 cm.
490 1  $a Cambridge tracts in mathematics ; $v 209
504    $a Includes bibliographical references (pages 344-360) and index.
505 00 $g 7.5. $t Bibliographical Notes. $g 1.1. $t Random Walks -- $g 1.2. $t Simple Random Walk -- $g 1.3. $t Lamperti's Problem -- $g 1.4. $t General Random Walk -- $g 1.5. $t Recurrence and Transience -- $g 1.6. $t Angular Asymptotics -- $g 1.7. $t Centrally Biased Random Walks -- $t Bibliographical Notes -- $g 2. $t Semimartingale Approach and Markov Chains -- $g 2.1. $t Definitions -- $g 2.2. $t An Introductory Example -- $g 2.3. $t Fundamental Semimartingale Facts -- $g 2.4. $t Displacement and Exit Estimates -- $g 2.5. $t Recurrence and Transience Criteria for Markov Chains -- $g 2.6. $t Expectations of Hitting Times and Positive Recurrence -- $g 2.7. $t Moments of Hitting Times -- $g 2.8. $t Growth Bounds on Trajectories -- $t Bibliograpical Notes -- $g 3. $t Lamperti's Problem -- $g 3.1. $t Introduction -- $g 3.2. $t Markovian Case -- $g 3.3. $t General Case -- $g 3.4. $t Lyapunov Functions -- $g 3.5. $t Recurrence Classification -- $g 3.6. $t Irreducibility and Regeneration -- $g 3.7. $t Moments and Tails of Passage Times -- $g 3.8. $t Excursion Durations and Maxima -- $g 3.9. $t Almost-Sure Bounds on Trajectories -- $g 3.10. $t Transient Theory in the Critical Case -- $g 3.11. $t Nullity and Weak Limits -- $g 3.12. $t Supercritical Case -- $g 3.13. $t Proofs for the Markovian Case -- $t Bibliographical Notes -- $g 4. $t Many-Dimensional Random Walks -- $g 4.1. $t Introduction -- $g 4.2. $t Elliptic Random Walks -- $g 4.3. $t Controlled Driftless Random Walks -- $g 4.4. $t Centrally Biased Random Walks -- $g 4.5. $t Range and Local Time of Many-Dimensional Martingales -- $t Bibliographical Notes -- $g 5. $t Heavy Tails -- $g 5.1. $t Chapter Overview -- $g 5.2. $t Directional Transience -- $g 5.3. $t Oscillating Random Walk -- $t Bibliographical Notes -- $g 6. $t Further Applications -- $g 6.1. $t Random Walk in Random Environment -- $g 6.2. $t Random Strings in Random Environment -- $g 6.3. $t Stochastic Billiards -- $g 6.4. $t Exclusion and Voter Models -- $t Bibliographical Notes -- $g 7. $t Markov Chains in Continuous Time -- $g 7.1. $t Introduction and Notation -- $g 7.2. $t Recurrence and Transience -- $g 7.3. $t Existence and Non-existence of Moments of Passage Times -- $g 7.4. $t Explosion and Implosion -- $g 7.5. $t Applications -- $t Bibliographical Notes.
520    $a Stochastic 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.-- $c Provided by Publisher.
650  0 $a Random walks (Mathematics)
650  0 $a Stochastic processes.
700 1  $a Popov, Serguei, $d 1972- $e author.
700 1  $a Wade, Andrew $q (Andrew R.), $d 1981- $e author.
773 18 $w 990002616320102756 $t Cambridge tracts in mathematics. $g no:no. 209
830  0 $a Cambridge tracts in mathematics $v 209.
941    $a 2
952    $l OVUX522 $d 20190212011942.0
952    $l USUX851 $d 20180703025457.0
956    $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=4F267466C38A11E7B100357297128E48
994    $a C0 $b IWA