The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, Kahane-Khintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γ-Radonifying operators, γ-boundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.
- Subject:
- Mathematics
- Material Type:
- Full Course
- Lecture Notes
- Provider:
- Delft University of Technology
- Provider Set:
- Delft University OpenCourseWare
- Author:
- Delft University Opencourseware
- Date Added:
- 07/05/2018