Related papers: Balls-in-bins with feedback and Brownian Motion
We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak…
Robot learning of real-world manipulation tasks remains challenging and time consuming, even though actions are often simplified by single-step manipulation primitives. In order to compensate the removed time dependency, we additionally…
Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
The binary branching Brownian motion in the boundary case is a particle system on the real line behaving as follows. It starts with a unique particle positioned at the origin at time $0$. The particle moves according to a Brownian motion…
Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along…
We first study a $d$-dimensional branching Brownian motion (BBM) among mild Poissonian obstacles, where a random trap field in $\mathbb{R}^d$ is created via a Poisson point process. The trap field consists of balls of fixed radius centered…
Using structures of Abstract Wiener Spaces, we define a fractional Brownian field indexed by a product space $(0,1/2] \times L^2(T,m)$, $(T,m)$ a separable measure space, where the first coordinate corresponds to the Hurst parameter of…
We study stationary fluctuations in two models involving $N$ Brownian particles undergoing stochastic resetting to the origin in 1d. We start with the basic reset model where the particles reset independently (model A). Then we introduce…
We consider a (one-dimensional) branching Brownian motion process with a general offspring distribution having at least two moments, and in which all particles have a drift towards the origin where they are immediately absorbed. It is…
This paper suggests a perfect-information game, along the lines of Levy's characterization of Brownian motion, that formalizes the process of Brownian motion in game-theoretic probability. This is perhaps the simplest situation where…
The first-exit time process of an inverse Gaussian L\'evy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and the tail probabilities decay exponentially. These…
We present a new simple method for rounding a semidefinite programming relaxation of a constraint satisfaction problem. We apply it to the problem of approximate angular synchronization. Specifically, we are given directed distances on a…
We study the persistence exponent for the first passage time of a random walk below the trajectory of another random walk. More precisely, let $\{B_n\}$ and $\{W_n\}$ be two centered, weakly dependent random walks. We establish that…
We consider the continuous time symmetric random walk with a slow bond on $\mathbb Z$, which rates are equal to $1/2$ for all bonds, except for the bond of vertices $\{-1,0\}$, which associated rate is given by $\alpha n^{-\beta}/2$, where…
Let $B=(B_t)_{t\in {\mathbb{R}}}$ be a two-sided standard Brownian motion. An unbiased shift of $B$ is a random time $T$, which is a measurable function of $B$, such that $(B_{T+t}-B_T)_{t\in {\mathbb{R}}}$ is a Brownian motion independent…
Under some weak conditions, the first-passage time of the Brownian motion to a continuous curved boundary is an almost surely finite stopping time. Its probability density function (pdf) is explicitly known only in few particular cases.…
Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian.…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
An analysis is presented of a Brownian particle moving on the half-line, subject to a restoring force proportional to its displacement and an absorbing boundary at the origin. When the initial displacement is large, the central moments of…