LEADER 04597nam 22007575 450 001 9910299988903321 005 20230628185916.0 010 $a1-4939-1323-9 024 7 $a10.1007/978-1-4939-1323-7 035 $a(CKB)3710000000306054 035 $a(SSID)ssj0001386795 035 $a(PQKBManifestationID)11764682 035 $a(PQKBTitleCode)TC0001386795 035 $a(PQKBWorkID)11374571 035 $a(PQKB)11036031 035 $a(DE-He213)978-1-4939-1323-7 035 $a(MiAaPQ)EBC6314316 035 $a(MiAaPQ)EBC5576244 035 $a(Au-PeEL)EBL5576244 035 $a(OCoLC)899248876 035 $a(PPN)183096096 035 $a(EXLCZ)993710000000306054 100 $a20141119d2014 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic Processes and Applications $eDiffusion Processes, the Fokker-Planck and Langevin Equations /$fby Grigorios A. Pavliotis 205 $a1st ed. 2014. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2014. 215 $a1 online resource (XIII, 339 p. 29 illus., 23 illus. in color.) 225 1 $aTexts in Applied Mathematics,$x0939-2475 ;$v60 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4939-1322-0 320 $aIncludes bibliographical references (pages 321-334) and index. 327 $aStochastic Processes -- Diffusion Processes -- Introduction to Stochastic Differential Equations -- The Fokker-Planck Equation -- Modelling with Stochastic Differential Equations -- The Langevin Equation -- Exit Problems for Diffusions -- Derivation of the Langevin Equation -- Linear Response Theory -- Appendix A Frequently Used Notations -- Appendix B Elements of Probability Theory. 330 $aThis book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes. 410 0$aTexts in Applied Mathematics,$x0939-2475 ;$v60 606 $aProbabilities 606 $aPartial differential equations 606 $aMechanics 606 $aMechanics, Applied 606 $aMathematical physics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aTheoretical and Applied Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15001 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 615 0$aProbabilities. 615 0$aPartial differential equations. 615 0$aMechanics. 615 0$aMechanics, Applied. 615 0$aMathematical physics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aPartial Differential Equations. 615 24$aTheoretical and Applied Mechanics. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a515.4 700 $aPavliotis$b Grigorios A$4aut$4http://id.loc.gov/vocabulary/relators/aut$0311134 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299988903321 996 $aStochastic processes and applications$91410668 997 $aUNINA