LEADER 03665nam 22006495 450 001 9910300545303321 005 20250413124803.0 010 $a3-319-90515-5 024 7 $a10.1007/978-3-319-90515-0 035 $a(CKB)3810000000358877 035 $a(DE-He213)978-3-319-90515-0 035 $a(MiAaPQ)EBC6310549 035 $a(PPN)229493947 035 $a(EXLCZ)993810000000358877 100 $a20180613d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTheory and Simulation of Random Phenomena $eMathematical Foundations and Physical Applications /$fby Ettore Vitali, Mario Motta, Davide Emilio Galli 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XIII, 235 p. 5 illus.) 225 1 $aUNITEXT for Physics,$x2198-7890 311 08$a3-319-90514-7 320 $aIncludes bibliographical references. 327 $a1 Review of Probability Theory -- 2 Applications to Mathematical Statistics -- 3 Conditional Probability and Conditional Expectation -- 4 Markov Chains -- 5 Sampling of Random Variables and Simulation -- 6 Brownian Motion -- 7 Introduction to Stochastic Calculus and Ito Integral -- 8 Introduction to Stochastic Differential Equations and Applications -- Bibliography -- Solutions. . 330 $aThe purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory. 410 0$aUNITEXT for Physics,$x2198-7890 606 $aMathematical physics 606 $aProbabilities 606 $aStatistics 606 $aMathematical Methods in Physics 606 $aProbability Theory 606 $aStatistical Theory and Methods 606 $aMathematical Physics 606 $aTheoretical, Mathematical and Computational Physics 615 0$aMathematical physics. 615 0$aProbabilities. 615 0$aStatistics. 615 14$aMathematical Methods in Physics. 615 24$aProbability Theory. 615 24$aStatistical Theory and Methods. 615 24$aMathematical Physics. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a519.2 700 $aVitali$b Ettore$4aut$4http://id.loc.gov/vocabulary/relators/aut$0835575 702 $aMotta$b Mario$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aGalli$b Davide Emilio$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300545303321 996 $aTheory and Simulation of Random Phenomena$92544854 997 $aUNINA