Wiesinger, Sven: Uniqueness of solutions to Fokker-Planck equations related to singular SPDE driven by Levy and cylindrical Wiener noise. 2011
Inhalt
- Introduction
- Framework and main results
- Framework and notation
- Spaces of functions and measures
- The test function space W-TA
- Spaces of probability kernels eta on H
- Hypotheses and main results
- The linear case
- The generalized Mehler semigroup S-t
- The infinitesimal generator U of S-t
- The generalized Mehler semigroup in C(0,T,C-u1)
- A core for V
- Regular nonlinearity F
- The transition evolution operators P-t
- Extension of the generator L-0
- Existence of a solution to the Fokker-Planck equation
- m-dissipativity of L
- Uniqueness results for the singular case
- m-dissipative nonlinearity F
- Regular approximations of F
- m-dissipativity of L
- Uniqueness of the solution to the Fokker-Planck equation
- Measurable nonlinearity F
- Example
- pi-semigroups
- m-dissipative maps and their Yosida approximation
- Zusammenfassung
- Index of notation