Related papers: First Passage Time Densities through H\"older curv…
We study the transition density of a standard two-dimensional Brownian motion killed when hitting a bounded Borel set $A$. We derive the asymptotic form of the density, say $p^A_t({\bf x},{\bf y})$, for large times $t$ and for ${\bf x}$ and…
We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…
The purpose of this article is threefold. First, we introduce a new type of boundary condition for the multiplicative-noise stochastic heat equation on the half space. This is essentially a Dirichlet boundary condition but with a nontrivial…
We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…
We study the statistical properties of first-passage time functionals of a one dimensional Brownian motion in the presence of stochastic resetting. A first-passage functional is defined as $V=\int_0^{t_f} Z[x(\tau)]$ where $t_f$ is the…
We find explicit upper bounds for the density of marginals of continuous diffusions where we assume that the diffusion coefficient is constant and the drift is solely assumed to be progressively measurable and locally bounded. In one…
We study the density of the signature of fractional Brownian motions with parameter $H>1/4$. In particular, we prove existence, smoothness, global Gaussian upper bounds and Varadhan's type asymptotics for this density. A key result is that…
We analyze the rate of convergence of the local statistics of Dyson Brownian motion to the GOE/GUE for short times $t=o(1)$ with deterministic initial data V . Our main result states that if the density of states of $V$ is bounded both…
Denote by $H(t)=(H_1(t),...,H_N(t))$ a function in $t\in{\mathbb{R}}_+^N$ with values in $(0,1)^N$. Let $\{B^{H(t)}(t)\}=\{B^{H(t)}(t),t\in{\mathbb{R}}^N_+\}$ be an $(N,d)$-multifractional Brownian sheet (mfBs) with Hurst functional $H(t)$.…
We present a classical, mesoscopic derivation of the Fokker-Planck equation for diffusion in an expanding medium. To this end, we take a conveniently generalized Chapman-Kolmogorov equation as the starting point. We obtain an analytical…
We construct and study branching fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. The construction relies on a generalization of the discrete approximation of fractional Brownian motion (Hammond and Sheffield, Probability…
We derive P(M,t_m), the joint probability density of the maximum M and the time t_m at which this maximum is achieved for a class of constrained Brownian motions. In particular, we provide explicit results for excursions, meanders and…
We study the fluctuation properties of the local time density, ${\rho _T} = \frac{1}{T}\int_0^T {\delta ( {r(t) - 1} )} dt$, spent by a $d$-dimensional Brownian particle at a spherical shell of unit radius, where $r(t)$ denotes the radial…
In this paper we derive quantitative boundary H\"older estimates, with explicit constants, for the inhomogeneous Poisson problem in a bounded open set $D\subset \mathbb{R}^d$. Our approach has two main steps: firstly, we consider an…
The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusions processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially…
The original density is 1 for $t\in (0,1)$, $b$ is an integer base ($b\geq 2$%), and $p\in (0,1)$ is a parameter. The first construction stage divides the unit interval into $b$ subintervals and multiplies the density in each subinterval by…
We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we…
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…
We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We derive a sufficient condition on r(t)…
We study a system of $n$ differential equations, each in dimension $d$. Only the first equation is forced by a Brownian motion and the dependence structure is such that, under a local weak H\"ormander condition, the noise propagates to the…