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Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics)

Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics)
Ioannis Karatzas Springer Engineering Books English Paperback 9780387976556
MRP: Rs 4369
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9780387976556
Paperback
Rs 4369
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Pages : 470
Release Date : 28 September 2004
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Dimension : 15.49 x 2.84 x 23.5 cm
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ISBN-10/SKU/ASIN : 0387976558
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A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time 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.

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