Brownian Motion and Stochastic Calculus
 Book
 1987
 #Probability
Book
A graduatecourse text, written for readers familiar with measuretheoretic probability and discretetime processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale...
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Number of Pages: 470
ISBN: 0387976558
ISBN13: 9780387976556
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A graduatecourse text, written for readers familiar with measuretheoretic probability and discretetime processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.