Related papers: Approximating the first passage time density from …

This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…

Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…

We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain…

We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the…

This paper considers the class of L\'evy processes that can be written as a Brownian motion time changed by an independent L\'evy subordinator. Examples in this class include the variance gamma model, the normal inverse Gaussian model, and…

We derive an approximate but fully explicit formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape in a general elongated domain in the plane. Our approximation combines conformal mapping, boundary…

The main result of this article regards a small time approximation for the Girsanov's exponential. We prove that the latter is well described over short time intervals by the solution of a deterministic partial differential equation.The…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

The Schr\"odinger integral-equation approach for calculating the classical first-passage time (C-fpt) probability density is extended to the case of quantum first-passage time (Q-fpt). Using this extension, we have calculated analytically…

We give a {\em deterministic} algorithm for approximately computing the fraction of Boolean assignments that satisfy a degree-$2$ polynomial threshold function. Given a degree-2 input polynomial $p(x_1,\dots,x_n)$ and a parameter $\eps >…

This paper develops a new technique for the path approximation of one-dimensional stochastic processes, more precisely the Brownian motion and families of stochastic differential equations sharply linked to the Brownian motion (usually…

We propose two methods for computing the large deviations of the first-passage-time statistics in general open quantum systems. The first method determines the region of convergence of the joint Laplace transform and the $z$-transform of…

First passage time (FPT) theory is often used to estimate timescales in cellular and molecular biology. While the overwhelming majority of studies have focused on the time it takes a given single Brownian searcher to reach a target,…

In this paper we study some aspects of search for an immobile target by a swarm of N non-communicating, randomly moving searchers (numbered by the index k, k = 1, 2,..., N), which all start their random motion simultaneously at the same…

We consider the problem of computing L1-distances between every pair ofcprobability densities from a given family. We point out that the technique of Cauchy random projections (Indyk'06) in this context turns into stochastic integrals with…

This paper is devoted to the computations of some relevant quantities associated with the free unitary Brownian motion. Using the Lagrange inversion formula, we first derive an explicit expression for its alternating star cumulants of even…

The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener…

An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…

Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of…

Making use of a Rice-like series expansion, for a class of stationary Gaussian processes the asymptotic behavior of the first passage time probability density function through certain time-varying boundaries, including periodic boundaries,…