Existence and uniqueness of solutions for Fokker–Planck equations on Hilbert spaces

By Vladimir Bogachev, Giuseppe Da Prato, Michael Röckner. 2009

49 citations recorded by the source corpus.

We consider a stochastic differential equation in a Hilbert space with time-dependent coefficients for which no general existence and uniqueness results are known. We prove, under suitable assumptions, the existence and uniqueness of a measure valued solution, for the corresponding Fokker–Planck equation. In particular, we verify the Chapman–Kolmogorov equations and get an evolution system of transition probabilities for the stochastic dynamics informally given by the stochastic differential equation.

Subfields: Control and Systems Engineering, Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3dbae4c071f9840d745fadb60282cec7cfd08656

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Franco Flandoli
2. Michael Röckner
3. Giuseppe Da Prato
4. Alexander Yur'evich Veretennikov
5. Xicheng Zhang
6. Feng-Yu Wang
7. Longjie Xie
8. Enrico Priola

In Finance

1. Michael Röckner
2. Giuseppe Da Prato
3. Franco Flandoli
4. Alexander Yur'evich Veretennikov
5. Feng-Yu Wang
6. Xicheng Zhang
7. Wei Liu
8. Massimiliano Gubinelli

In Statistical and Nonlinear Physics

1. Franco Flandoli
2. Giuseppe Da Prato
3. Michael Röckner
4. Alexander Yur'evich Veretennikov

Citations in the corpus

• Strong uniqueness for SDEs in Hilbert spaces with nonregular drift (2014, result): “That this process satisfies (57) follows from results in [BDR10].”