Related papers: A pursuit problem for squared Bessel processes

We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…

We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the…

We consider in this paper a non work-conserving Generalized Processor Sharing (GPS) system composed of two queues with Poisson arrivals and exponential service times. Using general results due to Fayolle \emph{et al}, we first establish the…

We propose a new approach to the problem of the first passage time. Our method is applicable not only to the Wiener process but also to the non--Gaussian L$\acute{\rm e}$vy flights or to more complicated stochastic processes whose…

We study first-passage properties for a particle that diffuses either inside or outside of generalized paraboloids, defined by y=a(x_1^2+...+x_{d-1}^2)^{p/2} where p>1, with absorbing boundaries. When the particle is inside the paraboloid,…

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that…

Consider two independent Goldstein-Kac telegraph processes $X_1(t)$ and $X_2(t)$ on the real line $\Bbb R$. The processes $X_k(t), \; k=1,2,$ are performed by stochastic motions at finite constant velocities $c_1>0, \; c_2>0,$ that start at…

This paper studies two related stochastic processes driven by Brownian motion: the Cox-Ingersoll-Ross (CIR) process and the Bessel process. We investigate their shared and distinct properties, focusing on time-asymptotic growth rates,…

We obtain explicit solutions for the density $\varphi_T$ of the first-time $T$ that a one-dimensional Brownian process $B$ reaches the twice, continuously differentiable moving boundary $f$ and such that $f''(t)\geq 0$ for all $t\in…

For some discrete parameters $k\ge0$, multivariate (Dunkl-)Bessel processes on Weyl chambers $C$ associated with root systems appear as projections of Brownian motions without drift on Euclidean spaces $V$, and the associated transition…

Although visual search appears largely random, several oculomotor biases exist such that the likelihoods of saccade directions and lengths depend on the previous scan path. Compared to the most recent fixations, the impact of the longer…

First-passage time problems are ubiquitous across many fields of study including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, first-passage time…

The relationship between anomalous superdiffusive behavior and particle trapping probability is analyzed on a rocking ratchet potential with spatially correlated weak disorder. The trapping probability density is shown, analytically and…

Let $n$ particles move in standard Brownian motion in one dimension, with the process terminating if two particles collide. This is a specific case of Brownian motion constrained to stay inside a Weyl chamber; the Weyl group for this…

We consider the one-dimensional squared Bessel process given by the stochastic differential equation (SDE) \begin{align*} dX_t = 1\,dt + 2\sqrt{X_t}\,dW_t, \quad X_0=x_0, \quad t\in[0,1], \end{align*} and study strong (pathwise)…

Let $B=\{(B_{t}^{1},..., B_{t}^{d}), t\geq 0\}$ be a $d$-dimensional fractional Brownian motion with Hurst parameter $H$ and let $R_{t}=% \sqrt{(B_{t}^{1})^{2}+... +(B_{t}^{d})^{2}}$ be the fractional Bessel process. It\^{o}'s formula for…

For a L\'evy process $X$ on a finite time interval consider the probability that it exceeds some fixed threshold $x>0$ while staying below $x$ at the points of a regular grid. We establish exact asymptotic behavior of this probability as…

The crossing probability in the time direction is defined for an off-equilibrium reaction-diffusion system as the probability that the system of size L is still active at time t, in the finite-size scaling limit. Exact results are obtained…

We consider Bernoulli first-passage percolation on the $d$-dimensional hypercubic lattice with $d \geq 2$. The passage time of edge $e$ is $0$ with probability $p$ and $1$ with probability $1-p$, independently of each other. Let $p_c$ be…

The motion of weakly inertial Brownian particles, transported by steady two-dimensional fluid flows, is investigated by means of asymptotic methods. We focus on the phenomenon of noise-induced separatrix crossing, which can force particles…