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Viser: Basic Stochastic Processes - A Course Through Exercises
Basic Stochastic Processes
A Course Through Exercises
Zdzislaw Brzezniak og Tomasz Zastawniak
(2000)
Sprog: Engelsk
Detaljer om varen
- 1. Udgave
- Paperback
- Udgiver: Springer London, Limited (Juli 2000)
- Forfattere: Zdzislaw Brzezniak og Tomasz Zastawniak
- ISBN: 9783540761754
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 Doob's Martingale Inequalities. -
4.
2 Doob's 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.
2.
1 Exponential Distribution and Lack of Memory. -
6.
2.
2 Construction of the Poisson Process. -
6.
2.
3 Poisson Process Starts from Scratch at Time t. -
6.
2.
4 Various Exercises on the Poisson Process. -
6.
3 Brownian Motion. -
6.
3.
1 Definition and Basic Properties. -
6.
3.
2 Increments of Brownian Motion. -
6.
3.
3 Sample Paths. -
6.
3.
4 Doob's Maximal L2 Inequality for Brownian Motion. -
6.
3.
5 Various Exercises on Brownian Motion. -
6.
4 Solutions. -
7. It? Stochastic Calculus. -
7.
1 It? Stochastic Integral: Definition. -
7.
2 Examples. -
7.
3 Properties of the Stochastic Integral. -
7.
4 Stochastic Differential and It? Formula. -
7.
5 Stochastic Differential Equations. -
7.
6 Solutions.