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SUMMARY:Some existence and uniqueness result for infinite dimensional Fokk
 er--Planck equations - Da Prato\, G (Scuola Normale Superiore di Pisa)
DTSTART:20120910T085000Z
DTEND:20120910T094000Z
UID:TALK39626@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We are here concerned with a Fokker--Planck equation in a sepa
 rable Hilbert space $H$ of the form egin{equation} label{e1} int_{0}^Tint
 _H mathcal K_0^F\,u(t\,x)\,mu_t(dx)dt=-int_H u(0\,x)\,zeta(dx)\,quadorall
 \;uinmathcal E nd{equation} The unknown is a probability kernel $(mu_t)_{
 tin [0\,T]}$. Here $K_0^F$ is the Kolmogorov operator $$ K_0^Fu(t\,x)=D_tu
 (t\,x)+rac12mbox{Tr}\;[BB^*D^2_xu(t\,x)]+langle Ax+F(t\,x)\,D_xu(t\,x)\na
 ngle $$ where $A:D(A) ubset H	o H$ is self-adjoint\, $F:[0\,T]	imes D(F)	o
  H$ is nonlinear and $mathcal E$ is a space of suitable test functions. $K
 _0^F$ is related to the stochastic PDE egin{equation} label{e2} dX=(AX+F(
 t\,X))dt+BdW(t) X(0)=x. nd{equation} We present some existence and unique
 ness results for equation (1) both when problem (2) is well posed and when
  it is not. \n
LOCATION:Seminar Room 1\, Newton Institute
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