Related papers: Brownian sheet and reflectionless potentials
We establish an integral test describing the exact cut-off between recurrence and transience for normally reflected Brownian motion in certain unbounded domains in a class of warped product manifolds. Besides extending a previous result by…
We discuss chains of interacting Brownian motions. Their time reversal invariance is broken because of asymmetry in the interaction strength between left and right neighbor. In the limit of a very steep and short range potential one arrives…
We define weighted fractional Brownian sheets, which are a class of Gaussian random fields with four parameters that include fractional Brownian sheets as special cases, and we give some of their properties. We show that for certain values…
In proving large deviation estimates, the lower bound for open sets and upper bound for compact sets are essentially local estimates. On the other hand, the upper bound for closed sets is global and compactness of space or an exponential…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation…
This manuscript provides an in-depth exploration of Brownian Motion, a fundamental stochastic process in probability theory for Biostatisticians. It begins with foundational definitions and properties, including the construction of Brownian…
The effective diffusion of Brownian particles in periodic potential has been a central topic in nonequilibrium statistical physcis. A classical result is the Lifson formula which provides the effective diffusion constant in periodic…
Let $\rho$ be compactly supported on $D \subset \mathbb R^2$. Endow $\mathbb R^2$ with the metric $e^{\rho}(dx_1^2 + dx_2^2)$. As $\delta \to 0$ the set of Brownian loops centered in $D$ with length at least $\delta$ has measure…
We consider a space-time continuous directed polymer in random environment. The path is Brownian and the medium is Poissonian. We review many results obtained in the last decade, and also we present new ones. In this fundamental setup, we…
It is well-known that Brownian ratchets can exhibit current reversals, wherein the sign of the current switches as a function of the driving frequency. We introduce a spatial discretization of such a two-dimensional Brownian ratchet to…
We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between $d$-dimensional partitions and $d$-dimensional arrays of nonnegative integers. This bijection…
We introduce and study a new random surface which we call the hyperbolic Brownian plane and which is the near-critical scaling limit of the hyperbolic triangulations constructed in arXiv:1401.3297. The law of the hyperbolic Brownian plane…
In this paper we establish an estimate for the rate of convergence of the Krasnosel'ski\v{\i}-Mann iteration for computing fixed points of non-expansive maps. Our main result settles the Baillon-Bruck conjecture [3] on the asymptotic…
By the work of P. L\'evy, the sample paths of the Brownian motion are known to satisfy a certain H\"older regularity condition almost surely. This was later improved by Ciesielski, who studied the regularity of these paths in Besov and…
We study the problem of Brownian motion in a multiscale potential. The potential is assumed to have N+1 scales (i.e. N small scales and one macroscale) and to depend periodically on all the small scales. We show that for nonseparable…
Motivated by a problematic coming from mathematical finance, this paper is devoted to existing and additional results of continuity and differentiability of the It\^o map associated to rough differential equations. These regularity results…
We consider the area of spheres centered at the distinguished point in the Brownian plane. As a function of the radius, the resulting process has continuously differentiable sample paths. Furthermore, the pair consisting of the process and…
We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends…
The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem due…