An Introduction to Continuous-Time Stochastic Processes - Vincenzo Capasso David Bakstein Gebunden

This textbook now in its third 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 the work features concrete examples of modeling real-world problems from biology medicine industrial applications finance and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: Markov processes Stochastic differential equations Arbitrage-free markets and financial derivatives Insu rance risk Population dynamics and epidemics Agent-based models New to the Third Edition: Infinitely divisible distributions Random measures Levy processes Fractional Brownian motion Ergodic theory Karhunen-Loeve expansion Additional applications Additional exercises Smoluchowski approximation of Langevin systems An Introduction to Continuous-Time Stochastic Processes Third Edition will be of interest to a broad audience of students pure and applied mathematicians and researchers and practitioners in mathematical finance biomathematics biotechnology and engineering. Suitable as a textbook for graduate or undergraduate courses as well as European Masters courses (according to the two-year-long second cycle of the Bologna Scheme) the work may also be used for self-study or as a reference. 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. From reviews of previous editions: The book is ... an account of fundamental concepts as they appear in relevant modern applications and literature. ... The book addresses three main groups: first mathematicians working in a different field second other scientists and professionals from a business or academic background third graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and or applications. -Zentralblatt MATH