Related papers: Intrinsic Ultracontractivity for Non-symmetric Lev…

We introduce the bounded packing property for a subgroup of a countable discrete group G. This property gives a finite upper bound on the number of left cosets of the subgroup that are pairwise close in G. We establish basic properties of…

We study the long time asymptotics of probability density functions (pdfs) of L\'{e}vy flights in different confining potentials. For that we use two models: Langevin - driven and (L\'{e}vy - Schr\"odinger) semigroup - driven dynamics. It…

We consider nonnegative solutions of a parabolic equation in a cylinder $D \timesI$, where $D$ is a noncompact domain of a Riemannian manifold and $I =(0,T)$ with $0 < T \le \infty$ or $I=(-\infty,0)$. Under the assumption [SSP] (i.e., the…

Let $X$ be a $n$-dimensional Ornstein-Uhlenbeck process, solution of the S.D.E. $$\d X_t = AX_t \d t + \d B_t$$ where $A$ is a real $n\times n$ matrix and $B$ a L\'evy process without Gaussian part. We show that when $A$ is non-singular,…

We establish metastability in the sense of Lebowitz and Penrose under practical and simple hypothesis for (families of) Markov chains on finite configuration space in some asymptotic regime, including the case of configuration space size…

The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…

We provide integral formulae for the Laplace transform of the entrance law of the reflected excursions for symmetric L\'evy processes in terms of their characteristic exponent. For subordinate Brownian motions and stable processes we…

This short note shows a limiting behavior of integrals of some centered antipersistent stationary infinitely divisible moving averages as the compact integration domain in $d\ge 1$ dimensions extends to the whole positive quadrant…

By constructing a coupling with unbounded time-dependent drift, dimension-free Harnack inequalities are established for a large class of stochastic differential equations with multiplicative noise. These inequalities are applied to the…

In the recent article D\"oring et al. [4] the authors conditioned a stable process with two-sided jumps to avoid an interval. As usual the strategy was to find an invariant function for the process killed on entering the interval and to…

Small-space and large-time estimates and asymptotic expansion of the distribution function and (the derivatives of) the density function of hitting times of points for symmetric L\'evy processes are studied. The L\'evy measure is assumed to…

We study hypercontractivity for the underdamped Langevin dynamics with a convex confining potential. Unlike in the overdamped case, the noise acts only on the velocity variable, so the usual argument based on the logarithmic Sobolev…

For every non-hyper-FC-central countable amenable group and every $k\geq 2$, we provide a sequence of symmetric, fully supported probability measures such that their convex combination is non-Liouville (that is it admits a non-constant…

The Sobolev regularity of invariant measures for diffusion processes is proved on non-smooth metric measure spaces with synthetic lower Ricci curvature bounds. As an application, the symmetrizability of semigroups is characterized, and the…

We prove the finiteness of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms where the center direction has a dominated decomposition into one dimensional bundle and there is a uniform lower bound for the absolute…

We obtain a representation of an inhomogeneous Levy process in a Lie group or a homogeneous space in terms of a drift, a matrix function and a measure function. Because the stochastic continuity is not assumed, our result generalizes the…

We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…

In this paper we prove a uniform and scale invariant boundary Harnack principle at infinity for a large class of purely discontinuous Feller processes on metric measure spaces.

In this paper, we discuss hypercontractivity for the Markov semigroup $P_t$ which is generated by segment processes associated with a range of functional SDEs of neutral type. As applications, we also reveal that the semigroup $P_t$…

Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive L\'evy process with non-zero L\'evy measure. In this paper we study the asymptotic behavior of the local time process,…