Related papers: A clever (self-repelling) burglar
The area swept out under a one-dimensional Brownian motion till its first-passage time is analysed using a backward Fokker-Planck technique. We obtain an exact expression of the area distribution for the zero drift case, and provide various…
In this paper we prove a large deviation principle for the empirical drift of a one-dimensional Brownian motion with self-repellence called the Edwards model. Our results extend earlier work in which a law of large numbers, respectively, a…
Let $X$ be a linear diffusion and $f$ a non-negative, Borel measurable function. We are interested in finding conditions on $X$ and $f$ which imply that the perpetual integral functional $$ I^X_\infty(f):=\int_0^\infty f(X_t) dt $$ is…
Self-interacting random walks (SIRWs) show long-range memory effects that result from the interaction of the random walker at time $t$ with the territory already visited at earlier times $t'<t$. This class of non-Markovian random walks has…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
A defender dispatches patrollers to circumambulate a perimeter to guard against potential attacks. The defender decides on the time points to dispatch patrollers and each patroller's direction and speed, as long as the long-run rate…
We develop the self similarity argument known as sparse domination in an abstract martingale setting, using a continuous time parameter. With this method, we prove a sharp weighted L^p estimate for the maximal operator Y^* of Y with respect…
When quantifying the time spent in the transient of a complex dynamical system, the fundamental problem is that for a large class of systems the actual time for reaching an attractor is infinite. Common methods for dealing with this problem…
This paper has two main results, which are connected through the fact that the first is a key ingredient in the second. Both are extensions of results concerning directional transience of nearest-neighbor random walks in random environments…
We study the norm of the two-dimensional Brownian motion conditioned to stay outside the unit disk at all times. By conditioning the process is changed from barely recurrent to slightly transient. We obtain sharp results on the rate of…
The problems considered in the present paper have their roots in two different cultures. The 'true' (or myopic) self-avoiding walk model (TSAW) was introduced in the physics literature by Amit, Parisi and Peliti. This is a nearest neighbor…
Self-repelling two-leg (biped) spider walk is considered where the local stochastic movements are governed by two independent control parameters $ \beta_d$ and $ \beta_h $, so that the former controls the distance ($ d $) between the legs…
We study the first-passage-time (FPT) properties of active Brownian particles to reach an absorbing wall in two dimensions. Employing a perturbation approach we obtain exact analytical predictions for the survival and FPT distributions for…
In the random acceleration process a point particle moving in one dimension is accelerated by Gaussian white noise with zero mean. Although several fundamental statistical properties of the motion have been analyzed in detail, the…
Let $(B_t)_{0\leq t\leq T}$ be either a Bernoulli random walk or a Brownian motion with drift, and let $M_t:=\max\{B_s: 0\leq s\leq t\}$, $0\leq t\leq T$. This paper solves the general optimal prediction problem \sup_{0\leq\tau\leq…
Let X_t be a subordinate Brownian motion, and suppose that the Levy measure of the underlying subordinator has completely monotone density. Under very mild conditions, we find integral formulae for the tail distribution P(\tau_x > t) of…
The "time-and-band limiting" commutative property was found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's, and independently by M. Mehta and later by C. Tracy and H. Widom in Random matrix theory. The…
We prove large deviations principles in large time, for the Brownian occupation time in random scenery. The random scenery is constant on unit cubes, and consist of i.i.d. bounded variables, independent of the Brownian motion. This model is…
We prove an invariance principle for the bridge of a random walk conditioned to stay positive, when the random walk is in the domain of attraction of a stable law, both in the discrete and in the absolutely continuous setting. This includes…
For a stochastic process $(X_t)_{t\geq 0}$ we establish conditions under which the inverse first-passage time problem has a solution for any random variable $\xi >0$. For Markov processes we give additional conditions under which the…