Stochastic Calculus and Applications

Stochastic Calculus and Applications by Samuel N. Cohen, Robert J. Elliott.

Completely revised and greatly expanded, 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 work...

Full description

Saved in:
Bibliographic Details
Main Authors: Cohen, Samuel N. (Author), Elliott, Robert J. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Birkhäuser, 2015.
Edition:2nd ed. 2015.
Series:Probability and Its Applications,
Springer eBook Collection.
Subjects:
Probabilities.
Partial differential equations.
Electrical engineering.
Computer mathematics.
Economics, Mathematical .
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Part I: Measure Theoretic Probability
  • Measure Integral
  • Probabilities and Expectation
  • Part II: Stochastic Processes
  • Filtrations, Stopping Times and Stochastic Processes
  • Martingales in Discrete Time
  • Martingales in Continuous Time
  • The Classification of Stopping Times
  • The Progressive, Optional and Predicable -Algebras
  • Part III: Stochastic Integration
  • Processes of Finite Variation
  • The Doob-Meyer Decomposition
  • The Structure of Square Integrable Martingales
  • Quadratic Variation and Semimartingales
  • The Stochastic Integral
  • Random Measures
  • Part IV: Stochastic Differential Equations
  • Ito's Differential Rule
  • The Exponential Formula and Girsanov's Theorem
  • Lipschitz Stochastic Differential Equations
  • Markov Properties of SDEs
  • Weak Solutions of SDEs
  • Backward Stochastic Differential Equations
  • Part V: Applications
  • Control of a Single Jump
  • Optimal Control of Drifts and Jump Rates
  • Filtering. Part VI: Appendices.

Similar Items