Related papers: Two-sided Green function estimates for killed subo…
We study the asymptotic behaviour of the time-changed stochastic process $\vphantom{X}^f\!X(t)=B(\vphantom{S}^f\!S (t))$, where $B$ is a standard one-dimensional Brownian motion and $\vphantom{S}^f\!S$ is the (generalized) inverse of a…
We consider processes which have the distribution of standard Brownian motion (in the forward direction of time) starting from random points on the trajectory which accumulate at $-\infty$. We show that these processes do not have to have…
Let $X$ be an isotropic unimodal L\'{e}vy jump process on $\mathbb{R}^d$. We develop probabilistic methods which in many cases allow us to determine whether $X$ satisfies the elliptic Harnack inequality (EHI), by looking only at the jump…
In this article subordination of random walks in $R^d$ is considered. We prove that subordination of random walks in the sense of [BSC12] yields the same process as subordination of L\'evy processes (in the sense of Bochner). Furthermore,…
The strong $L^2$-approximation of occupation time functionals is studied with respect to discrete observations of a $d$-dimensional c\`adl\`ag process. Upper bounds on the error are obtained under weak assumptions, generalizing previous…
By using the coupling argument, we establish the Harnack and log-Harnack inequalites for stochastic differential equations with non-Lipschitz drifts and driven by additive anisotropic subordinated Brownian motions (in particular,…
Our aim in this article is to provide explicit computable estimates for the cumulative distribution function (c.d.f.) and the $p$-th order moment of the exponential functional of a fractional Brownian motion (fBM) with drift. Using…
The main objective of the work is to provide sharp two-sided estimates of $\lambda$-Green function of hyperbolic Brownian motion of a half-space. We strongly rely on recent results obtained by K. Bogus and J. Malecki [3], regarding precise…
In this paper, we establish sharp two-sided estimates for the Green functions of non-symmetric diffusions with measure-valued drifts in bounded Lipschitz domains. As consequences of these estimates, we get a 3G type theorem and a…
Let $(X,\mathcal W)$ be a balayage space, $1\in \mathcal W$, or - equivalently - let $\mathcal W$ be the set of excessive functions of a Hunt process on a locally compact space $X$ with countable base such that $\mathcal W$ separates…
We study a discrete model of the Laplacian in $\mathbb{R}^2$ that preserves the geometric structure of the original continual object. This means that, speaking of a discrete model, we do not mean just the direct replacement of differential…
For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the…
The Green functions of the partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian manifold are investigated via the heat kernel methods. We study the resolvent of a special class of…
We discuss subordination of random compact R-trees. We focus on the case of the Brownian tree, where the subordination function is given by the past maximum process of Brownian motion indexed by the tree. In that particular case, the…
In this paper, we derive global sharp heat kernel estimates for symmetric alpha-stable processes (or equivalently, for the fractional Laplacian with zero exterior condition) in two classes of unbounded C^{1,1} open sets in R^d:…
We prove a connection between the Green's function of the fractional Anderson model and the two point function of a self-avoiding random walk with long range jumps, adapting a strategy proposed by Schenker in 2015. This connection allows us…
Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…
We study the spectral heat content for a class of open sets with fractal boundaries determined by similitudes in $\mathbb{R}^{d}$, $d\geq 1$, with respect to subordinate killed Brownian motions via $\alpha/2$-stable subordinators and…
We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…
The points of the closed range of a drift-free subordinator with no killing are used for separating into blocks the elements of a sample of size $n$ from the standard exponential distribution. This gives rise to a random composition of $n$.…