Related papers: How many paths to simulate correlated Brownian mot…
This article is devoted to methods of construction and study of stochastic models based on Monte Carlo method. A model of Brownian motion, the construction and processing which brings to a world of random numbers and mathematical…
In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization…
We give potential theoretic estimates for the probability that a set $A$ contains a double point of planar Brownian motion run for unit time. Unlike the probability for $A$ to intersect the range of a Markov process, this cannot be…
We study a correlated Brownian motion in two dimensions, which is reflected, stopped or killed in a wedge represented as the intersection of two half spaces. First, we provide explicit density formulas, hinted by the method of images. These…
We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-intersections. We provide a formal definition of shortest boundary paths for…
We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a personal computer. The…
(I) We prove that the (maximum) number of monotone paths in a geometric triangulation of $n$ points in the plane is $O(1.7864^n)$. This improves an earlier upper bound of $O(1.8393^n)$; the current best lower bound is $\Omega(1.7003^n)$.…
Convergence of directed forests, spanning on random subsets of lattices or on point processes, towards the Brownian web has made the subject of an abundant literature, a large part of which relies on a criterion proposed by Fontes, Isopi,…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…
We present the first exact simulation method for multidimensional reflected Brownian motion (RBM). Exact simulation in this setting is challenging because of the presence of correlated local-time-like terms in the definition of RBM. We…
Finding optimal reaction coordinates and predicting accurate kinetic rates for activated processes are two of the foremost challenges of molecular simulations. We introduce an algorithm that tackles the two problems at once: starting from a…
We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give series expansions…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
In this paper, we develop a theory of common decomposition for two correlated Brownian motions, in which, by using change of time method, the correlated Brownian motions are represented by a triplet of processes, $(X,Y,T)$, where $X$ and…
This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths…
We have developed an efficient information-maximization method for computing the optimal shapes of tuning curves of sensory neurons by optimizing the parameters of the underlying feedforward network model. When applied to the problem of…
We describe a novel algorithm for rounding packing integer programs based on multidimensional Brownian motion in $\mathbb{R}^n$. Starting from an optimal fractional feasible solution $\bar{x}$, the procedure converges in polynomial time to…
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…
We describe a simple numerical simulation, suitable for an undergraduate project (or graduate problem set), of the Brownian motion of a particle in a Hooke-law potential well. Understanding this physical situation is a practical necessity…
We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…