Stochastic Calculus and Applications

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... Ausführliche Beschreibung

1. Person: Cohen, Samuel N.
Weitere Körperschaften: SpringerLink (Online service)
Weitere Personen: Elliott, Robert J. [author]
Format: E-Buch
Sprache: English
Veröffentlicht: New York, NY Springer New York 2015, 2015
Beschreibung: XXIII, 666 p. 17 illus online resource
Ausgabe: 2nd ed. 2015
Serien: Probability and Its Applications
Schlagworte: Probability Theory and Stochastic Processes
Electrical engineering
Computational Mathematics and Numerical Analysis
Partial Differential Equations
Computer mathematics
Economics, Mathematical
Electrical Engineering
Partial differential equations
Quantitative Finance
Mathematics
Probabilities
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Inhaltsangabe:
  • 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

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