This comprehensive guide to stochastic processes gives a complete
overview of the theory and addresses the most important
applications. Pitched at a level accessible to beginning graduate
students and researchers from applied disciplines, it is both a
course book and a rich resource for individual readers. Subjects
covered include Brownian motion, stochastic calculus, stochastic
differential equations, Markov processes, weak convergence of
processes and semigroup theory. Applications include the
Black-Scholes formula for the pricing of derivatives in financial
mathematics, the Kalman-Bucy filter used in the US space program
and also theoretical applications to partial differential equations
and analysis. Short, readable chapters aim for clarity rather than
full generality. More than 350 exercises are included to help
readers put their new-found knowledge to the test and to prepare
them for tackling the research literature.
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