G-expectations in infinite dimensional spaces and related PDEs (2013)
Abstract
In this thesis, we extend the G-expectation theory to infinite dimensions. Such notions as a covariation set of G-normal distributed random variables, viscosity solution, a stochastic integral drive by G-Brownian motion are introduced and described in the given infinite dimensional case. We also give a probabilistic representation of the unique viscosity solution to the fully nonlinear parabolic PDE with unbounded first order term in Hilbert space in terms of G-expectation theory.
hilbert space – g-expectation – upper expectation – g-brownian motion – g-stochastic integral – b-continuity – viscosity solution – itô's isometry inequality – bdg inequality – fully nonlinear pde – ornstein-uhlenbeck process.
Information
- Author
- Ibragimov, Anton
- Institution
- Università degli Studi di Milano-Bicocca
- Supervisor
- Publication Year
- 2013
- Upload Date
- June 13, 2013
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