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 Insurance 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
