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Stochastic calculus and applications / Samuel N. Cohen and Robert J. Elliott.

By: Contributor(s): Material type: TextTextSeries: Probability and its applicationsPublication details: New York : Birkhauser, 2015.Edition: 2nd edDescription: xxiii, 666 p. : illustrations ; 24 cmISBN:
  • 9781493928668 (hbk : acidfree paper)
Subject(s): DDC classification:
  • 519.23 23 C678
Contents:
Part I: Measure Theoretic Probability.- 1. Measure Integral.- 2. Probabilities and Expectation.- Part II: Stochastic Processes.- 3. Filtrations, Stopping Times and Stochastic Processes.- 4. Martingales in Discrete Time.- 5. Martingales in Continuous Time.- 6. The Classification of Stopping Times.- 7. The Progressive, Optional and Predicable -Algebras.- Part III: Stochastic Integration.- 8. Processes of Finite Variation.- 9. The Doob-Meyer Decomposition.- 10. The Structure of Square Integrable Martingales.- 11. Quadratic Variation and Semimartingales.- 12. The Stochastic Integral.- 13. Random Measures.- Part IV: Stochastic Differential Equations.- 14. Ito's Differential Rule.- 15. The Exponential Formula and Girsanov's Theorem.- 16. Lipschitz Stochastic Differential Equations.- 17. Markov Properties of SDEs.- 18. Weak Solutions of SDEs.- 19. Backward Stochastic Differential Equations.- Part V: Applications.- 20. Control of a Single Jump.- 21. Optimal Control of Drifts and Jump Rates.- 22. Filtering. Appendices.
Summary: The new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry.
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Includes bibliographical references and index.

Part I: Measure Theoretic Probability.-
1. Measure Integral.-
2. Probabilities and Expectation.-
Part II: Stochastic Processes.-
3. Filtrations, Stopping Times and Stochastic Processes.-
4. Martingales in Discrete Time.-
5. Martingales in Continuous Time.-
6. The Classification of Stopping Times.-
7. The Progressive, Optional and Predicable -Algebras.-
Part III: Stochastic Integration.-
8. Processes of Finite Variation.-
9. The Doob-Meyer Decomposition.-
10. The Structure of Square Integrable Martingales.-
11. Quadratic Variation and Semimartingales.-
12. The Stochastic Integral.-
13. Random Measures.-
Part IV: Stochastic Differential Equations.-
14. Ito's Differential Rule.-
15. The Exponential Formula and Girsanov's Theorem.-
16. Lipschitz Stochastic Differential Equations.-
17. Markov Properties of SDEs.-
18. Weak Solutions of SDEs.-
19. Backward Stochastic Differential Equations.-
Part V: Applications.-
20. Control of a Single Jump.-
21. Optimal Control of Drifts and Jump Rates.-
22. Filtering.
Appendices.

The new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry.

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