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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.

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