Related papers: On subhamonicity for symmetric Markov processes

We characterize the complexity functions of subshifts up to asymptotic equivalence. The complexity function of every aperiodic function is non-decreasing, submultiplicative and grows at least linearly. We prove that conversely, every…

In this paper, we combine tools from pluripotential theory and commutative algebra to study singularity invariants of plurisubharmonic functions. We establish several relationships between the singularity invariants of plurisubharmonic…

On a general open set of the euclidean space, we study the relation between the embedding of the homogeneous Sobolev space $\mathcal{D}^{1,p}_0$ into $L^q$ and the summability properties of the distance function. We prove that in the…

In this paper, we consider the Sub-Laplacian L which consists of sum of squares of smooth vector fields that satisfy Hormander's finite rank condition. We study the Dirichlet problem for this operator on domains that satisfy certain…

Motivated by recent results regarding the equivalence of the Dirichlet and Neumann problems for the Laplace operator in the case of simply connected regions, the present paper takes a step further and provides a similar equivalence between…

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…

We consider Markov decision processes with synchronizing objectives, which require that a probability mass of $1-\epsilon$ accumulates in a designated set of target states, either once, always, infinitely often, or always from some point…

Based on the needs of convergence proofs of preconditioned proximal point methods, we introduce notions of partial strong submonotonicity and partial (metric) subregularity of set-valued maps. We study relationships between these two…

We consider the problem of drawing samples from posterior distributions formed under a Dirichlet prior and a truncated multinomial likelihood, by which we mean a Multinomial likelihood function where we condition on one or more counts being…

First, we solve a crucial problem under which conditions increasing uniform K-monotonicity is equivalent to lower locally uniform K-monotonicity. Next, we investigate properties of substochastic operators on $L^1+L^\infty$ with…

In this paper we solve the Dirichlet problems for different classes of plurisubharmonic functions on compact sets in $\mathbb C^n$ including continuous, pluriharmonic and maximal functions.

In a recent paper of Akhunzhanov and Shatskov the two-dimensional Dirichlet spectrum with respect to Euclidean norm was defined. We consider an analogous definition for arbitrary norms on $\mathbb{R}^2$ and prove that, for each such norm,…

We give some relationships between the first Dirichlet eigenvalues and the exit time moments for the general symmetric Markov processes. As applications, we present some examples, including symmetric diffusions and $\alpha$-stable…

This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer…

We prove an intrinsic equivalence between strong hypercontractivity and a strong logarithmic Sobolev inequality for the cone of logarithmically subharmonic functions. We introduce a new large class of measures, Euclidean regular and…

The goal of this paper has two-folds. First, we establish skeleton and spine decompositions for superprocesses whose underlying processes are general symmetric Hunt processes. Second, we use these decompositions to obtain weak and strong…

Given a frequency $\lambda$, we study general Dirichlet series $\sum a_n e^{-\lambda_n s}$. First, we give a new condition on $\lambda$ which ensures that a somewhere convergent Dirichlet series defining a bounded holomorphic function in…

We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…

We describe a generalization of the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) which is able to encode prior information that state transitions are more likely between "nearby" states. This is accomplished by defining a…

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…