Related papers: Quickest Search over Brownian Channels
The distribution for the minimum of Brownian motion or the Cauchy process is well-known using the reflection principle. Here we consider the problem of finding the sample-by-sample minimum, which we call the online minimum search. We…
We consider an optimal control problem, where a Brownian motion with drift is sequentially observed, and the sign of the drift coefficient changes at jump times of a symmetric two-state Markov process. The Markov process itself is not…
Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of L\'evy walks, a specific range of optimal efficiencies was suggested under variation of search…
In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift…
We study the efficiency of random search processes based on L{\'e}vy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the bias of the searcher…
An unbiased shift of the two-sided Brownian motion $(B_t \colon t\in{\mathbb R})$ is a random time $T$ such that $(B_{T+t} \colon t\in{\mathbb R})$ is still a two-sided Brownian motion. Given a pair $\mu, \nu$ of orthogonal probability…
In this paper we study an incomplete information optimal switching problem in which the manager only has access to noisy observations of the underlying Brownian motion $\{W_t\}_{t \geq 0}$. The manager can, at a fixed cost, switch between…
In the present paper, we consider that $N$ diffusion processes $X^1,\dots,X^N$ are observed on $[0,T]$, where $T$ is fixed and $N$ grows to infinity. Contrary to most of the recent works, we no longer assume that the processes are…
Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einstein's theory of Brownian motion, however, is only applicable at long time scales. At short…
We study a simple singular control problem for a Brownian motion with constant drift and variance reflected at the origin. Exerting control pushes the process towards the origin and generates a concave increasing state-dependent yield which…
One century after Einstein's work, Brownian Motion still remains both a fundamental open issue and a continous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic…
Considering the paradigmatic driven Brownian motion, we perform extensive numerical analysis on the performance of optimal linear-response processes far from equilibrium. We focus on the overdamped regime where exact optimal processes are…
In this paper we study the drifted Brownian meander, that is a Brownian motion starting from $ u $ and subject to the condition that $ \min_{ 0\leq z \leq t} B(z)> v $ with $ u > v $. The limiting process for $ u \downarrow v $ is analyzed…
At fast timescales, the self-similarity of random Brownian motion is expected to break down and be replaced by ballistic motion. So far, an experimental verification of this prediction has been out of reach due to a lack of instrumentation…
Brownian motion is the perpetual irregular motion exhibited by small particles immersed in a fluid. Such random motion of the particles is produced by statistical fluctuations in the collisions they suffer with the molecules of the…
We consider optimal stopping problems for a Brownian motion and a geometric Brownian motion with a "disorder", assuming that the moment of a disorder is uniformly distributed on a finite interval. Optimal stopping rules are found as the…
We study the efficiency of search processes based on Levy flights (LFs) with power-law distributed jump lengths in the presence of an external drift. While LFs turn out to be efficient search processes when relative to the starting point…
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 solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
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…