Related papers: Generating stochastic trajectories with global dyn…
We demonstrate that the conventional path integral formulations generate inconsistent results exemplified by the geometric Brownian motion under the general stochastic interpretation. We thus develop a novel path integral formulation for…
The main contribution of this paper is a novel method for planning globally optimal trajectories for dynamical systems subject to polygonal constraints. The proposed method is a hybrid trajectory planning approach, which combines graph…
Effective understanding of the environment and accurate trajectory prediction of surrounding dynamic obstacles are critical for intelligent systems such as autonomous vehicles and wheeled mobile robotics navigating in complex scenarios to…
The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation.…
We study an inverse first-passage-time problem for Wiener process $X(t)$ subject to hold and jump from a boundary $c.$ Let be given a threshold $S>X(0) \ge c,$ and a distribution function $F$ on $[0, + \infty ).$ The problem consists in…
We discuss the stochastic process of creation and annihilation of particles, i.e., the $A^{n} \rightleftarrows B$ process in which $n$ particles $A$s and one particle $B$ are transformed to each other. Considering the case that the…
In this paper we introduce spatiotemporal constraints for trajectories, i.e., restrictions that the trajectory must be in some part of the state space (spatial constraint) at some point in time (temporal constraint). Spatiotemporal…
We show that the initial value problem for Hamilton-Jacobi equations with multiplicative rough time dependence, typically stochastic, and convex Hamiltonians satisfies finite speed of propagation. We prove that in general the range of…
Random walks on dynamic graphs have received increasingly more attention from different academic communities over the last decade. Despite the relatively large literature, little is known about random walks that construct the graph where…
We develop an information-theoretic formulation of stochastic dynamics in which the fundamental stochastic variable is the total action connecting spacetime points, rather than individual paths. By maximizing Shannon entropy over a joint…
We study the distribution of occupation times for a one-dimensional random walk restricted to a finite interval by reflecting boundary conditions. At short times the classical bimodal distribution due to L\'evy is reproduced with walkers…
We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation \[dX_t=|X_t|^{\alpha} dW_t,\] where $W_t$ is a one-dimensional Brownian motion and $\alpha\in(0,1/2)$. Weak…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
We show by numerical simulations that a non rotationally symmetric body, whose orientation is fixed and whose center of mass can only slide along a rectilinear guide, under the effect of inelastic collisions with a surrounding gas of…
We introduce a scheme for deriving an optimally-parametrised Langevin dynamics of few collective variables from data generated in molecular dynamics simulations. The drift and the position-dependent diffusion profiles governing the Langevin…
In this paper, we present a novel strategy to compute minimum-time trajectories for quadrotors in constrained environments. In particular, we consider the motion in a given flying region with obstacles and take into account the physical…
An approach to analysis on path spaces of Riemannian manifolds is described. The spaces are furnished with `Brownian motion' measure which lies on continuous paths, though differentiation is restricted to directions given by tangent paths…
We consider the occupation area of spherical (fractional) Brownian motion, i.e. the area where the process is positive, and show that it is uniformly distributed. For the proof, we introduce a new simple combinatorial view on occupation…
Trajectory prediction (TP) plays an important role in supporting the decision-making of Air Traffic Controllers (ATCOs). Traditional TP methods are deterministic and physics-based, with parameters that are calibrated using aircraft…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…