Related papers: Continuity of the Revuz correspondence under the a…
A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric…
The relationship between smooth measures and positive continuous additive functionals is well known, and this correspondence is called the Revuz correspondence. We investigate the relationships between several types of convergence of smooth…
We establish a formula for moments of certain random variables involving positive continuous additive functionals (PCAFs) of standard processes which have absolutely continuous transition functions and are in duality with standard processes…
In this paper, we prove that the laws of perturbed diffusion processes and perturbed reflected diffusion processes are absolutely continuous with respect to the Lebesgue measure. The main tool we use is the Malliavin calculus.
We provide necessary and sufficient conditions for the convergence of Revuz measures of finite energy integrals. More precisely, the Revuz map from the set of all smooth measures of finite energy integrals, equipped with the topology…
We consider a class of multi-type particle systems having similar structure to the contact process and show that additivity is equivalent to the existence of a dual process, extending a result of Harris. We give two additional…
We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the…
In this work, a mode of convergence for measurable functions is introduced. A related notion of Cauchy sequence is given and it is proved that this notion of convergence is complete in the sense that Cauchy sequences converge. Moreover, the…
We develop sufficient analytic conditions for conservativeness of non-sectorial perturbations of symmetric Dirichlet forms which can be represented through a carr\'e du champ on a locally compact separable metric space. These form an…
We investigate some analytic properties of traces of Dirichlet forms with respect to measures satisfying Hardy-type inequality. Among other results we prove convergence of spectra, ordered eigenvalues, eigenfunctions as well as convergence…
We study symmetric Dirichlet forms on metric measure spaces, which may possess both strongly local and pure-jump parts. We introduce a new formulation of a tail condition for jump measures and weighted functional inequalities. Our framework…
We provide explicit sufficient conditions for absolute continuity and equivalence between the distributions of two jump-diffusion processes that can explode and be killed by a potential.
Let $F$ be an entire function represented by absolutely convergent for all $z\in\mathbb{C}$ Dirichlet series of the form $ F(z) = \sum\nolimits_{n=0}^{+\infty} a_{n}e^{z\lambda_{n}},$\ where a sequence $(\lambda_n)$ such that…
We consider the correspondence assigning to every Radon measure on two Tychonoff coordinate spaces the set of probability measures with these marginals. It is proved that this correspondence is continuous.
We find conditions for stationary measures of random dynamical systems on surfaces having dissipative diffeomorphisms to be absolutely continuous. These conditions involve a uniformly expanding on average property in the future (UEF) and…
We show that, for disjoint domains in the Euclidean space, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries. This…
We show that, for disjoint domains in the Euclidean space whose boundaries satisfy a non-degeneracy condition, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and…
Diffusion models have made rapid progress in generating high-quality samples across various domains. However, a theoretical understanding of the Lipschitz continuity and second momentum properties of the diffusion process is still lacking.…
In this paper, we establish new quantitative convergence bounds for a class of functional autoregressive models in weighted total variation metrics. To derive our results, we show that under mild assumptions, explicit minorization and…
The Wright-Fisher diffusion is a fundamentally important model of evolution encompassing genetic drift, mutation, and natural selection. Suppose you want to infer the parameters associated with these processes from an observed sample path.…