Related papers: Approximate calculation of multidimensional first …
First passage time plays a fundamental role in dynamical characterization of stochastic processes. Crucially, our current understanding on the problem is almost entirely relies on the theoretical formulations, which assume the processes…
The analysis of dynamical systems is a fundamental tool in the natural sciences and engineering. It is used to understand the evolution of systems as large as entire galaxies and as small as individual molecules. With predefined conditions…
First-passage times provide invaluable insight into fundamental properties of stochastic processes. Yet, various forms of gating mask first-passage times and differentiate them from actual detection times. For instance, imperfect conditions…
An obvious way to simulate a L\'evy process $X$ is to sample its increments over time $1/n$, thus constructing an approximating random walk $X^{(n)}$. This paper considers the error of such approximation after the two-sided reflection map…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
Escape from a potential well is an extreme example of transient behavior. We consider the escape of the harmonically forced particle under viscous damping from the benchmark truncated weakly nonlinear potential well. Main attention is paid…
For one-dimensional linear kinetic equations analytical solutions of problems about moderately strong evaporation (condensation), when frequency of collisions of molecules is constant, are received . The equation and distribution function…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…
Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from…
An accurate algorithm is proposed to improve the prediction of a particle in collision with a moving wall within the direct simulation Monte Carlo (DSMC) framework for the simulation of unsteady rarefied flows. This algorithm is able to…
A {\em propagation-dispersion equation} is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the continuous limit of the {\em first visit equation}, an…
In this work we relate the density of the first-passage time of a Wiener process to a moving boundary with the three dimensional Bessel bridge process and a solution of the heat equation with a moving boundary. We provide bounds.
Two time scale stochastic approximation algorithms emulate singularly perturbed deterministic differential equations in a certain limiting sense, i.e., the interpolated iterates on each time scale approach certain differential equations in…
One of the most fundamental problems in Markov decision processes is analysis and control synthesis for safety and reachability specifications. We consider the stochastic reach-avoid problem, in which the objective is to synthesize a…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
Linear approximations of the AC power flow equations are of great significance for the computational efficiency of large-scale optimal power flow (OPF) problems. Put differently, the feasibility of the obtained solution is essential for…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
We show that the Laplace approximation of a supremum by Lp-norms has interesting consequences in optimization. For instance, the logarithmic barrier functions (LBF) of a primal convex problem P and its dual appear naturally when using this…
In this short paper, we consider discrete-time Markov chains on lattices as approximations to continuous-time diffusion processes. The approximations can be interpreted as finite difference schemes for the generator of the process. We…