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Change of time and change of measure / Ole E. Barndorff-Nielsen and Albert Shiryaev.

By: Contributor(s): Material type: TextTextSeries: Advanced series on statistical science and applied probability ; v 21.Publication details: Singapore : World Scientific, ©2015.Edition: 2nd edDescription: xviii, 326 p. ; 24 cmISBN:
  • 9789814678582 (hardcover : alk. paper)
Subject(s): DDC classification:
  • 519.23 23 B259
Contents:
1. Random Change of Time; 2. Integral Representations and Change of Time in Stochastic Integrals; 3. Semimartingales: Basic Notions, Structures, Elements of Stochastic Analysis; 4. Stochastic Exponential and Stochastic Logarithm. Cumulant Processes; 5. Processes with Independent Increments. Levy Processes; 6. Change of Measure. General Facts; 7. Change of Measure in Models Based on Levy Processes; 8. Change of Time in Semimartingale Models and Models Based on Brownian Motion and Levy Processes; 9. Conditionally Gaussian Distributions and Stochastic Volatility Models for the Discrete-time Case; 10. Martingale Measures in the Stochastic Theory of Arbitrage; 11. Change of Measure in Option Pricing; 12. Conditionally Brownian and Levy Processes. Stochastic Volatility Models; 13. A Wider View. Ambit Processes and Fields, and Volatility/Intermittency;
Summary: Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.
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Includes bibliographical references and index.

1. Random Change of Time;
2. Integral Representations and Change of Time in Stochastic Integrals;
3. Semimartingales: Basic Notions, Structures, Elements of Stochastic Analysis;
4. Stochastic Exponential and Stochastic Logarithm. Cumulant Processes;
5. Processes with Independent Increments. Levy Processes; 6. Change of Measure. General Facts;
7. Change of Measure in Models Based on Levy Processes;
8. Change of Time in Semimartingale Models and Models Based on Brownian Motion and Levy Processes;
9. Conditionally Gaussian Distributions and Stochastic Volatility Models for the Discrete-time Case;
10. Martingale Measures in the Stochastic Theory of Arbitrage; 11. Change of Measure in Option Pricing;
12. Conditionally Brownian and Levy Processes. Stochastic Volatility Models;
13. A Wider View. Ambit Processes and Fields, and Volatility/Intermittency;

Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.

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