LEADER 03111nam 22004815 450 001 9910254285503321 005 20230309191706.0 010 $a3-319-62310-9 024 7 $a10.1007/978-3-319-62310-8 035 $a(CKB)4100000000881620 035 $a(DE-He213)978-3-319-62310-8 035 $a(MiAaPQ)EBC5117960 035 $a(PPN)220125325 035 $a(EXLCZ)994100000000881620 100 $a20171031d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic processes /$fby Andrei N Borodin 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (XIV, 626 p. 1 illus.) 225 1 $aProbability and Its Applications,$x2297-0371 311 $a3-319-62309-5 320 $aIncludes bibliographical references and index. 327 $aPreface -- Notations -- Basic facts -- Stochastic calculus -- Distributions of functionals of Brownian motion -- Diffusion processes -- Brownian local time -- Diffusions with jumps -- Invariance principle for random walks and local times -- Appendix 1. Heat transfer problem -- Appendix 2. Special functions -- Appendix 3. Inverse Laplace transforms -- Appendix 4. Differential equations and their solutions -- Appendix 5. Examples of transformations of measures associated with diffusion processes -- Appendix 6. Formulae for n-fold differentiation -- Bibliography -- Subject index. 330 $aThis book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike. 410 0$aProbability and Its Applications,$x2297-0371 606 $aProbabilities 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aProbabilities. 615 14$aProbability Theory and Stochastic Processes. 676 $a519.2 700 $aBorodin$b A. N$4aut$4http://id.loc.gov/vocabulary/relators/aut$057188 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254285503321 996 $aStochastic Processes$91562456 997 $aUNINA