111 research outputs found
Existence and approximation of Hunt processes associated with generalized Dirichlet forms
We show that any strictly quasi-regular generalized Dirichlet form that
satisfies the mild structural condition D3 is associated to a Hunt process, and
that the associated Hunt process can be approximated by a sequence of
multivariate Poisson processes. This also gives a new proof for the existence
of a Hunt process associated to a strictly quasi-regular generalized Dirichlet
form that satisfies SD3 and extends all previous results.Comment: Revised, shortened and improved versio
On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets
We obtain a criterion for the quasi-regularity of generalized (non-sectorial)
Dirichlet forms, which extends the result of P.J. Fitzsimmons on the
quasi-regularity of (sectorial) semi-Dirichlet forms. Given the right (Markov)
process associated to a semi-Dirichlet form, we present sufficient conditions
for a second right process to be a standard one, having the same state space.
The above mentioned quasi-regularity criterion is then an application. The
conditions are expressed in terms of the associated capacities, nests of
compacts, polar sets, and quasi-continuity. A second application is on the
quasi-regularity of the generalized Dirichlet forms obtained by perturbing a
semi-Dirichlet form with kernels .Comment: Correction of typos and other minor change
Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
Let E be an unbounded open (or closed) domain in Euclidean space of dimension
greater or equal to two. We present conservativeness criteria for (possibly
reflected) diffusions with state space E that are associated to fairly general
perturbed divergence form operators. Our main tool is a recently extended
forward and backward martingale decomposition, which reduces to the well-known
Lyons-Zheng decomposition in the symmetric case.Comment: Corrected typos, minor modification
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