TIME-INHOMOGENEOUS DIFFUSIONS CORRESPONDING TOSYMMETRIC DIVERGENCE FORM OPERATORS
Andrzej Rozkosz
Abstract: We consider a time-inhomogeneous Markov family corresponding to a
symmetric uniformly elliptic divergence form operator. We show that for any in the
Sobolev space with if and if the additive
functional admits a unique strict decomposition into a
martingale additive functional of finite energy and a continuous additive functional of zero
energy. Moreover, we give a stochastic representation of the zero energy part and show that in
case the diffusion coefficient is regular in time the functional is a Dirichlet
process for each starting point The paper contains also rectifications of
incorrectly presented or incorrectly proved statements of our earlier paper [14].
corresponding to a
symmetric uniformly elliptic divergence form operator. We show that for any 
in the
Sobolev space 
with 
if 
and 
if 
the additive
functional 
admits a unique strict decomposition into a
martingale additive functional of finite energy and a continuous additive functional of zero
energy. Moreover, we give a stochastic representation of the zero energy part and show that in
case the diffusion coefficient is regular in time the functional 
is a Dirichlet
process for each starting point 
The paper contains also rectifications of
incorrectly presented or incorrectly proved statements of our earlier paper [14].