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We will show the central limit theorem for the general one-dimensional lattice where the space of symbols is a compact metric space. We consider the CLT for Lipschitz-Gibbs probabilities and in the proof we use several properties of the…
Consider a partition of $R^n$ into finitely many polyhedral regions $D_i$ and associated drift vectors $\mu_i\in R^n$. We study ``hybrid'' dynamical systems whose trajectories have a constant drift, $\dot x=\mu_i$, whenever $x$ is in the…
By using a general version of curvature condition, derivative inequalities are established for a large class of subelliptic diffusion semigroups. As applications, the Harnack/cost-entropy/cost-variance inequalities for the diffusion…
Point-to-point reflection holding for harmonic functions subject to the Dirichlet or Neumann conditions on an analytic curve in the plane almost always fails for solutions to more general elliptic equations. We develop a non-local,…
Let ${\cal E}$ be a Dirichlet form on $L_2(X)$ and $\Omega$ an open subset of $X$. Then one can define Dirichlet forms ${\cal E}_D$, or ${\cal E}_N$, corresponding to ${\cal E}$ but with Dirichlet, or Neumann, boundary conditions imposed on…
This paper concerns preservation of velocity and pressure equilibria in smooth, compressible, multicomponent flows in the inviscid limit. First, we derive the velocity-equilibrium and pressure-equilibrium conditions of a standard…
We show continuity in generalized weighted Morrey spaces of sub-linear integral operators generated by some classical integral operators and commutators. The obtained estimates are used to study global regularity of the solution of the…
We study Dirichlet process-based models for sets of predictor-dependent probability distributions, where the domain and predictor space are general Polish spaces. We generalize the definition of dependent Dirichlet processes, originally…
In this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical ($\alpha=1$) differential equation in the fractional case (here using fractional…
We provide a general construction scheme for $\mathcal L^p$-strong Feller processes on locally compact separable metric spaces. Starting from a regular Dirichlet form and specified regularity assumptions, we construct an associated…
We give a extensive account of a recent new way of applying the Dirichlet form theory to random Poisson measures. The main application is to obtain existence of density for thelaws of random functionals of L\'evy processes or solutions of…
This work provides an extension of parts of the classical finite dimensional sub-elliptic theory in the context of infinite dimensional compact connected metrizable groups. Given a well understood and well behaved bi-invariant Laplacian,…
We give three characterizations of the Dirichlet-type spaces $D(\mu)$. First we characterize $D(\mu)$ in terms of a double integral and in terms of the mean oscillation in the Bergman metric, none of them involve the use of derivatives.…
In a previous paper we developed a regularity and compactness theory in Euclidean ambient spaces for codimension 1 weakly stable CMC integral varifolds satisfying two (necessary) structural conditions. Here we generalize this theory to the…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
We study global properties of Dirichlet forms such as uniqueness of the Dirichlet extension, stochastic completeness and recurrence. We characterize these properties by means of vanishing of a boundary term in Green's formula for functions…
Using the standard tools of Daniell-Stone integrals, Stone-\v{C}ech compactification and Gelfand transform, we discuss how any Dirichlet form defined on a measurable space can be transformed into a regular Dirichlet form on a locally…
We continue our previous work studying critical exponent semilinear elliptic (and subelliptic) problems which generalize the classical Yamabe problem. In [3] the focus was on metric-measure spaces with an `almost smooth' structure, with…
We consider a degenerate/singular wave equation in one dimension, with drift and in presence of a leading operator which is not in divergence form. We impose a homogeneous Dirichlet boundary condition where the degeneracy occurs and a…
In this paper we study the asymptotic behavior of a family of discrete functionals as the lattice size, $\varepsilon>0$, tends to zero. We consider pairwise interaction energies satisfying $p$-growth conditions, $p<d$, $d$ being the…