Related papers: The frog model with drift on R
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…
For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at $x$ decays as $1/x$ as $x \to \infty$, we quantify degree of transience via existence of moments for conditional return…
This work considers a type of slow-fast system, where the slow component is driven by fractional Brownian motion with H > 1/2 and the fast component is a Markovian stationary process. Our solution mapping is defined based on the…
It is well known that standard one-dimensional Brownian motion B(t) has no isolated zeros almost surely. We show that for any alpha<1/2 there are alpha-H\"older continuous functions f for which the process B-f has isolated zeros with…
We address the dynamics of interacting particles on a disordered lattice formed by a random comb. The dynamics comprises that of the asymmetric simple exclusion process, whereby motion to nearest-neighour sites that are empty is more likely…
In this paper, we investigate a Brownian motion (BM) with purely time dependent drift and difusion by suggesting and examining several Brownian functionals which characterize the lifetime and reactivity of such stochastic processes. We…
We study a branching Brownian motion $Z$ in $\mathbb{R}^d$, among obstacles scattered according to a Poisson random measure with a radially decaying intensity. Obstacles are balls with constant radius and each one works as a trap for the…
We consider the motion of a particle on a Galton Watson tree, when the probabilities of jumping from a vertex to any one of its neighbours is determined by a random process. Given the tree, positive weights are assigned to the edges in such…
Consider a massive (inert) particle impinged from above by N Brownian particles that are instantaneously reflected upon collision with the inert particle. The velocity of the inert particle increases due to the influence of an external…
This paper is devoted to the detailed analysis of three-dimensional motions in $\mathbb{R}^3$ with orthogonal directions switching at Poisson times and moving with constant speed $c>0$. The study of the random position at an arbitrary time…
Let $B_s$ be a $d$-dimensional Brownian motion and $\omega(dx)$ be an independent Poisson field on $\mathbb{R}^d$. The almost sure asymptotics for the logarithmic moment generating function [\log\math…
The inverse first passage time problem asks whether, for a Brownian motion $B$ and a nonnegative random variable $\zeta$, there exists a time-varying barrier $b$ such that $\mathbb{P}\{B_s>b(s),0\leq s\leq t\}=\mathbb{P}\{\zeta>t\}$. We…
In the present paper, an expansion of the transition density of Hyperbolic Brownian motion with drift is given, which is potentially useful for pricing and hedging of options under stochastic volatility models. We work on a condition on the…
Let $B^{H}$ be a $d$-dimensional fractional Brownian motion with Hurst index $H\in(0,1)$, $f:[0,1]\longrightarrow\mathbb{R}^{d}$ a Borel function, and $E\subset[0,1]$, $F\subset\mathbb{R}^{d}$ are given Borel sets. The focus of this paper…
Rolling of a small sphere on a solid support is governed by a non-linear friction that is akin to the Coulombic dry fiction. No motion occurs when the external field is weaker than the frictional resistance. However, with the intervention…
Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape…
In this paper, we introduce a spatial model for dormancy in random environment via a two-type branching random walk in continuous-time, where individuals can switch between dormant and active states through spontaneous switching independent…
Rationally independent free fermions are those where sums of single-particle energies multiplied by arbitrary rational coefficients vanish only if the coefficients are all zero. This property guaranties that they have no degeneracies in the…
We prove that the probability the frog model with death and drift on the $d$-ary tree is recurrent can be made positive and thus is not monotone in the drift parameter.
The Brownian web is a random object that occurs as the scaling limit of an infinite system of coalescing random walks. Perturbing this system of random walks by, independently at each point in space-time, resampling the random walk…