arXiv subjects

Gerald Trutnau

Publications and source records attributed to Gerald Trutnau.

24 records · Page 2Linked to original sources

arXiv2011

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.

math.PR↗

arXiv2011

Pathwise uniqueness of the squared Bessel and CIR processes with skew reflection on a deterministic time dependent curve

We investigate pathwise uniqueness for the squared Bessel and Cox-Ingersoll-Ross processes with additional reflection term that is multiplied by some real number strictly between minus one and one. The reflection term is the symmetric local time of the corresponding processes at a deterministic time dependent curve.

math.PR↗

arXiv2011

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.

math.PR↗

arXiv2011

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 .

math.PR↗

arXiv2009

Weak existence of the squared Bessel process and CIR process with skew reflection on a deterministic time dependent curve

Using the technique of moving domains, and classical direct stochastic calculus, we construct the Cox-Ingersoll-Ross process, as well as its square root, with additional skew reflection on a deterministic time dependent curve.

math.PR↗

arXiv2007

Some Parabolic Pdes Whose Drift is an Irregular Random Noise in Space

A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a probabilistic interpretation is investigated.

math.PR↗