Brownian motion and stochastic calculus

By: Ioannis KaratzasMaterial type: TextTextSeries: Graduate Texts in Mathematics ; Vol. 113Publication details: USA: Springer, [c1998]Edition: 2nd edDescription: 470 pISBN: 9780387976556Subject(s): MathematicsLOC classification: QA274.75Online resources: Click here to access online
Contents:
1. Martingales, Stopping Times, and Filtrations 2. Brownian Motion 3. Stochastic Integration 4. Brownian Motion and Partial Differential Equations 5. Stochastic Differential Equations 6. P. Lévy’s Theory of Brownian Local Time
Summary: This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish 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. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). ---summary provided by publisher
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Book Book ICTS
Mathematic Rack No 5 QA274.75 (Browse shelf (Opens below)) Available Billno:IN 00562; Billdate: 2018-05-03 01141
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1. Martingales, Stopping Times, and Filtrations
2. Brownian Motion
3. Stochastic Integration
4. Brownian Motion and Partial Differential Equations
5. Stochastic Differential Equations
6. P. Lévy’s Theory of Brownian Local Time

This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish 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. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). ---summary provided by publisher

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