Related papers: How many paths to simulate correlated Brownian mot…
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a…
We present an efficient algorithm to multiply two hyperbolic octonions. The direct multiplication of two hyperbolic octonions requires 64 real multiplications and 56 real additions. More effective solutions still do not exist. We show how…
We give explicit parametric equations for all irreducible plane projective sextic curves which have at most double points and whose total Milnor number is maximal (is equal to 19). In each case we find a parametrization over a number field…
We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle…
The article shows a bridge representation for the joint density of a system of stochastic processes consisting of a Brownian motion with drift coupled with a correlated fractional Brownian motion with drift. As a result, a small time…
Computing collision-free trajectories is of prime importance for safe navigation. We present an approach for computing the collision probability under Gaussian distributed motion and sensing uncertainty with the robot and static obstacle…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
We derive integral formulas, involving the Airy function, for moments of the time a two-sided Brownian motion with parabolic drift attains its maximum.
Update rules for learning in dynamic time warping spaces are based on optimal warping paths between parameter and input time series. In general, optimal warping paths are not unique resulting in adverse effects in theory and practice. Under…
Let X and Y be two simple symmetric continuous-time random walks on the vertices of the n-dimensional hypercube. We consider the class of co-adapted couplings of these processes, and describe an intuitive coupling which is shown to be the…
The aim of the presented research is to give a rigorous mathematical approach to Feynman path integrals based on strong (pathwise) approximations based on simple random walks.
We obtain sharp asymptotic estimates for hitting probabilities of a critical branching Brownian motion in one dimension with killing at 0 We also obtain sharp asymptotic formulas for the tail probabilities of the number of particles killed…
A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…
Exact and asymptotic formulas relating to dynamical correlations for overdamped Brownian motion are obtained. These formulas include a generalization of the $f$-sum rule from the theory of quantum fluids, a formula relating the static…
Navigating our physical environment requires changing directions and turning. Despite its ecological importance, we do not have a unified theoretical account of non-straight-line human movement. Here, we present a unified optimality…
Stochastic shortest path computations are often performed under very strict time constraints, so computational efficiency is critical. A major determinant for the CPU time is the number of scenarios used. We demonstrate that by carefully…
Given starting and ending positions and velocities, $L_2$ bounds on the acceleration and velocity, and the restriction to no more than two constant control inputs, this paper provides routines to compute the minimal-time path. Closed form…
We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under…
We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times of Brownian motion subject to the constraint that the distribution of the stopping time is a…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…