TY - BOOK ID - 86044106 TI - An Introduction to Continuous-Time Stochastic Processes : Theory, Models, and Applications to Finance, Biology, and Medicine AU - Capasso, Vincenzo AU - Bakstein, David PY - 2021 SN - 3030696537 3030696529 PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Stochastic processes KW - Mathematical models. KW - Processos estocàstics KW - Models matemàtics KW - Models (Matemàtica) KW - Models experimentals KW - Models teòrics KW - Mètodes de simulació KW - Anàlisi de sistemes KW - Mètode de Montecarlo KW - Modelització multiescala KW - Models economètrics KW - Models lineals (Estadística) KW - Models multinivell (Estadística) KW - Models no lineals (Estadística) KW - Programació (Ordinadors) KW - Simulació per ordinador KW - Teoria de màquines KW - Models biològics KW - Càlcul estocàstic KW - Funcions aleatòries KW - Processos aleatoris KW - Probabilitats KW - Anàlisi estocàstica KW - Aproximació estocàstica KW - Camps aleatoris KW - Filtre de Kalman KW - Fluctuacions (Física) KW - Martingales (Matemàtica) KW - Processos de Markov KW - Processos de ramificació KW - Processos gaussians KW - Processos puntuals KW - Rutes aleatòries (Matemàtica) KW - Semimartingales (Matemàtica) KW - Sistemes estocàstics KW - Teoremes de límit (Teoria de probabilitats) KW - Teoria de cues KW - Teoria de l'estimació KW - Teoria de la predicció KW - Stochastic processes. KW - Stochastic models. KW - Social sciences KW - Biomathematics. KW - Stochastic Processes. KW - Stochastic Modelling. KW - Mathematical Modeling and Industrial Mathematics. KW - Mathematics in Business, Economics and Finance. KW - Mathematical and Computational Biology. KW - Mathematics. KW - Biology KW - Mathematics KW - Models, Mathematical KW - Simulation methods KW - Models, Stochastic KW - Mathematical models KW - Random processes KW - Probabilities UR - https://www.unicat.be/uniCat?func=search&query=sysid:86044106 AB - This 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 different fields. 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 differential 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. ER -