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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
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Stochastic Analysis (Hardcover, 1st ed. 2020)
Loot Price: R3,378
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Stochastic Analysis (Hardcover, 1st ed. 2020)
Series: Monographs in Mathematical Economics, 3
Expected to ship within 10 - 15 working days
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This book is intended for university seniors and graduate students
majoring in probability theory or mathematical finance. In the
first chapter, results in probability theory are reviewed. Then, it
follows a discussion of discrete-time martingales, continuous time
square integrable martingales (particularly, continuous martingales
of continuous paths), stochastic integrations with respect to
continuous local martingales, and stochastic differential equations
driven by Brownian motions. In the final chapter, applications to
mathematical finance are given. The preliminary knowledge needed by
the reader is linear algebra and measure theory. Rigorous proofs
are provided for theorems, propositions, and lemmas. In this book,
the definition of conditional expectations is slightly different
than what is usually found in other textbooks. For the Doob-Meyer
decomposition theorem, only square integrable submartingales are
considered, and only elementary facts of the square integrable
functions are used in the proof. In stochastic differential
equations, the Euler-Maruyama approximation is used mainly to prove
the uniqueness of martingale problems and the smoothness of
solutions of stochastic differential equations.
General
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