The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

Skip to content



Some existence and uniqueness result for infinite dimensional Fokker--Planck equations

Da Prato, G (Scuola Normale Superiore di Pisa)
Monday 10 September 2012, 09:50-10:40

Seminar Room 1, Newton Institute


We are here concerned with a Fokker--Planck equation in a separable Hilbert space $H$ of the form \begin{equation} \label{e1} \int_{0}^T\int_H \mathcal K_0^F\,u(t,x)\,\mu_t(dx)dt=-\int_H u(0,x)\,\zeta(dx),\quad\forall\;u\in\mathcal E \end{equation} The unknown is a probability kernel $(\mu_t)_{t\in [0,T]}$. Here $K_0^F$ is the Kolmogorov operator $$ K_0^Fu(t,x)=D_tu(t,x)+\frac12\mbox{Tr}\;[BB^*D^2_xu(t,x)]+\langle Ax+F(t,x),D_xu(t,x)\rangle $$ where $A:D(A)\subset H\to H$ is self-adjoint, $F:[0,T]\times D(F)\to H$ is nonlinear and $\mathcal E$ is a space of suitable test functions. $K_0^F$ is related to the stochastic PDE \begin{equation} \label{e2} dX=(AX+F(t,X))dt+BdW(t) X(0)=x. \end{equation} We present some existence and uniqueness results for equation (1) both when problem (2) is well posed and when it is not.


[pdf ]


The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

Back to top ∧