Stochastic Differential Equations - NDIR041
|
|
|
||
Last update: JSEIDLER/MFF.CUNI.CZ (15.05.2008)
|
|
||
Last update: T_KPMS (19.05.2008)
Students will learn basic results from the theory of stochastic differential equations.
|
|
||
Last update: JSEIDLER/MFF.CUNI.CZ (15.05.2008)
Karatzas, I., Shreve, S.E.: Brownian motion and stochastic calculus. Springer Verlag, Berlin, 1988
Krylov, N.V.: Introduction to the theory of diffusion processes. American Math. Society, Providence, 1995. |
|
||
Last update: G_M (28.05.2008)
Lecture. |
|
||
Last update: JSEIDLER/MFF.CUNI.CZ (15.05.2008)
1. The Burkholder-Davis-Gundy inequality.
2. Basic results on existence and uniqueness of strong solutions to equations with Lipschitz or locally Lipschitz coefficients. Khas'minskii's test for nonexplosions.
3. Linear equations.
4. Markovianity of solutions.
5. Representation of continuous martingales by stochastic integrals.
6. Exponential martingales nad Novikov's condition. |