Stochastic Analysis in Discrete and Continuous Settings [electronic resource] :With Normal Martingales / by Nicolas Privault.
by Privault, Nicolas [author.]; SpringerLink (Online service).
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BookSeries: Lecture Notes in Mathematics: 1982Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.Description: online resource.ISBN: 9783642023804.Subject(s): Mathematics | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic Processes | Game Theory, Economics, Social and Behav. SciencesDDC classification: 519.2 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| QA274-274.9 (Browse shelf) | Available | ||||
| Long Loan | MAIN LIBRARY | QA273.A1-274.9 (Browse shelf) | Available |
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The Discrete Time Case -- Continuous Time Normal Martingales -- Gradient and Divergence Operators -- Annihilation and Creation Operators -- Analysis on the Wiener Space -- Analysis on the Poisson Space -- Local Gradients on the Poisson Space -- Option Hedging in Continuous Time.
This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.
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