LEADER 05359nam 22007575 450 001 9910485588803321 005 20240213130819.0 010 $a3-030-69653-7 024 7 $a10.1007/978-3-030-69653-5 035 $a(CKB)5590000000487490 035 $a(MiAaPQ)EBC6644888 035 $a(Au-PeEL)EBL6644888 035 $a(OCoLC)1263871452 035 $a(DE-He213)978-3-030-69653-5 035 $a(PPN)258059672 035 $a(EXLCZ)995590000000487490 100 $a20210617d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn Introduction to Continuous-Time Stochastic Processes $eTheory, Models, and Applications to Finance, Biology, and Medicine /$fby Vincenzo Capasso, David Bakstein 205 $a4th ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2021. 215 $a1 online resource (574 pages) 225 1 $aModeling and Simulation in Science, Engineering and Technology,$x2164-3725 311 $a3-030-69652-9 327 $aForeword -- Preface to the Fourth Edition -- Preface to the Third Edition -- Preface to the Second Edition -- Preface -- Part I: Theory of Stochastic Processes -- Fundamentals of Probability -- Stochastic Processes -- The Itô Integral -- Stochastic Differential Equations -- Stability, Stationary, Ergodicity -- Part II: Applications of Stochastic Processes -- Applications to Finance and Insurance -- Applications to Biology and Medicine -- Measure and Integration -- Convergence of Probability Measures on Metric Spaces -- Diffusion Approximation of a Langevin System -- Elliptic and Parabolic Equations -- Semigroups of Linear Operators -- Stability of Ordinary Differential Equations -- References -- Nomenclature -- Index. 330 $aThis textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across di?erent ?elds. Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic di?erential equations. An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularly the applications explored in the second half of the book. 410 0$aModeling and Simulation in Science, Engineering and Technology,$x2164-3725 606 $aStochastic processes 606 $aStochastic models 606 $aMathematical models 606 $aSocial sciences$xMathematics 606 $aBiomathematics 606 $aStochastic Processes 606 $aStochastic Modelling 606 $aMathematical Modeling and Industrial Mathematics 606 $aMathematics in Business, Economics and Finance 606 $aMathematical and Computational Biology 606 $aProcessos estocāstics$2thub 606 $aModels matemātics$2thub 608 $aLlibres electrōnics$2thub 615 0$aStochastic processes. 615 0$aStochastic models. 615 0$aMathematical models. 615 0$aSocial sciences$xMathematics. 615 0$aBiomathematics. 615 14$aStochastic Processes. 615 24$aStochastic Modelling. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aMathematics in Business, Economics and Finance. 615 24$aMathematical and Computational Biology. 615 7$aProcessos estocāstics 615 7$aModels matemātics 676 $a519.2 700 $aCapasso$b Vincenzo$f1945-$051830 702 $aBakstein$b David$f1975- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910485588803321 996 $aAn Introduction to Continuous-Time Stochastic Processes$92504060 997 $aUNINA