Author | Brzeลบniak, Zdzisลaw. author |
---|---|
Title | Basic Stochastic Processes [electronic resource] : A Course Through Exercises / by Zdzisลaw Brzeลบniak, Tomasz Zastawniak |
Imprint | London : Springer London : Imprint: Springer, 1999 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-0533-6 |
Descript | X, 226 p. online resource |
1. Review of Probability -- 1.1 Events and Probability -- 1.2 Random Variables -- 1.3 Conditional Probability and Independence -- 1.4 Solutions -- 2. Conditional Expectation -- 2.1 Conditioning on an Event -- 2.2 Conditioning on a Discrete Random Variable -- 2.3 Conditioning on an Arbitrary Random Variable -- 2.4 Conditioning on a ?-Field -- 2.5 General Properties -- 2.6 Various Exercises on Conditional Expectation -- 2.7 Solutions -- 3. Martingales in Discrete -- 3.1 Sequences of Random Variables -- 3.2 Filtrations -- 3.3 Martingales -- 3.4 Games of Chance -- 3.5 Stopping Times -- 3.6 Optional Stopping Theorem -- 3.7 Solutions -- 4. Martingale Inequalities and Convergence -- 4.1 Doobโs Martingale Inequalities -- 4.2 Doobโs Martingale Convergence Theorem -- 4.3 Uniform Integrability and L1 Convergence of Martingales -- 4.4 Solutions -- 5. Markov Chains -- 5.1 First Examples and Definitions -- 5.2 Classification of States -- 5.3 Long-Time Behaviour of Markov Chains: General Case -- 5.4 Long-Time Behaviour of Markov Chains with Finite State Space -- 5.5 Solutions -- 6. Stochastic Processes in Continuous Time -- 6.1 General Notions -- 6.2 Poisson Process -- 6.3 Brownian Motion -- 6.4 Solutions -- 7. Itรด Stochastic Calculus -- 7.1 Itรด Stochastic Integral: Definition -- 7.2 Examples -- 7.3 Properties of the Stochastic Integral -- 7.4 Stochastic Differential and Itรด Formula -- 7.5 Stochastic Differential Equations -- 7.6 Solutions