Related papers: The Matsumoto and Yor process and infinite dimensi…
The isoperimetric inequalities for the expected lifetime of Brownian motion state that the $L^p$-norms of the expected lifetime in a bounded domain for $1\leq p\leq \infty$ are maximized when the region is a ball with the same volume. In…
Zabrodin recently proposed a generalization of Dyson Brownian motion to a setting where the particles are confined to a smooth Jordan curve in the plane. In this paper, we discuss a rigorous construction of such a process on a rectifiable…
The main purpose of this paper is to establish the existence, nonexistence and symmetry of nontrivial solutions to the higher order Brezis-Nirenberg problems associated with the GJMS operators $P_k$ on bounded domains in the hyperbolic…
The purpose of this work is to construct a {\it Brownian motion} with values in simplicial complexes with piecewise differential structure. In order to state and prove the existence of such Brownian motion, we define a family of continuous…
Let $ \{W(t), t\ge 0\}$ be a standard Brownian motion. If $I$ is a bounded interval on which $W $ has no zero, an almost sure lower bound to $\inf\{|W(t)|, t\in I\}$ can be provided, when $I$ is taken from a given countable family of…
We study relationships between asymptotic geometry of submanifolds in the hyperbolic space and their regularity properties near the ideal boundary, revisiting some of the related results in the literature. In particular, we discuss…
Pitman's theorem states that if {Bt, t $\ge$ 0} is a one-dimensional Brownian motion, then {Bt -- 2 inf s$\le$t Bs, t $\ge$ 0} is a three dimensional Bessel process, i.e. a Brownian motion conditioned in Doob sense to remain forever…
We study non-autonomous conformal iterated function systems, with finite or countably infinite alphabet alike. These differ from the usual (autonomous) iterated function systems in that the contractions applied at each step in time are…
For any natural number $d$, the Vladimirov-Taibleson operator is a natural analogue of the Laplace operator for complex-valued functions on a $d$-dimensional vector space $V$ over a local field $K$. Just as the Laplace operator on…
The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener…
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…
Let $M$ and $\tau$ be the supremum and its time of a L\'evy process $X$ on some finite time interval. It is shown that zooming in on $X$ at its supremum, that is, considering $((X_{\tau+t\varepsilon}-M)/a_\varepsilon)_{t\in\mathbb R}$ as…
This paper deals with some inequalities for trigonometric and hyperbolic functions such as the Jordan inequality and its generalizations. In particular, lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are proved.
We investigate the relationship between the metric boundary and the Gromov boundary of a hyperbolic metric space. We show that the Gromov boundary is a quotient topological space of the metric boundary, and that therefore a word-hyperbolic…
We consider an n-dimensional Brownian Motion trapped inside a bounded convex set by normally-reflecting boundaries. It is well-known that this process is uniformly ergodic. However, the rates of this ergodicity are not well-understood,…
We give general sufficient conditions which imply upper and lower bounds for the probability that a multiparameter process hits a given set E in terms of a capacity of E related to the process. This extends a result of Khoshnevisan and Shi…
The paths of Brownian motion have been widely studied in the recent years relatively in Besov spaces $B_{p, \infty}^\a$. The results are the same as to the Brownian bridge. In fact these regularities properties are established in some…
We show that a Brownian motion on $\mathbb{R}_{\ge 0}$ which is allowed to spend a total of $s > 0$ time units outside a bounded interval does not leave the interval at all. This can be seen as an extreme example of entropic repulsion.…
We study the boundary behavior of the Kobayashi-Royden metric and the Kobayashi hyperbolicity of domains in Riemannian manifolds. As an application, we prove a Fatou type theorem on the existence, almost everywhere, of non tangential limits…
Let $F_{BC}(\lambda,k;t)$ be the Heckman-Opdam hypergeometric function of type BC with multiplicities $k=(k_1,k_2,k_3)$ and weighted half sum $\rho(k)$ of positive roots. We prove that $F_{BC}(\lambda+\rho(k),k;t)$ converges for…