Related papers: Last Hitting Time Distributions for Solvable Diffu…
We present a backward diffusion flow (i.e. a backward-in-time stochastic differential equation) whose marginal distribution at any (earlier) time is equal to the smoothing distribution when the terminal state (at a latter time) is…
We study the multi-time distribution in a discrete polynuclear growth model or, equivalently, in directed last-passage percolation with geometric weights. A formula for the joint multi-time distribution function is derived in the discrete…
In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear…
A finite-time fluctuation theorem for the diffusion-influenced surface reaction A <=> B is investigated for spherical and Janus catalytic particles. The finite-time rates and thermodynamic force are analytically calculated by solving…
Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has…
We analyze the mean time t_{app} that a randomly moving particle spends in a bounded domain (sphere) before it escapes through a small window in the domain's boundary. A particle is assumed to diffuse freely in the bulk until it approaches…
The Hamilton-Jacobi-Bellman equation (HJB) associated with the time inhomogeneous singular control problem is a parabolic partial differential equation, and the existence of a classical solution is usually difficult to prove. In this paper,…
The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability... The usual procedure is to use discretiza-tion schemes…
We investigate first-hitting location (FHL) statistics induced by drift-diffusion processes in domains with absorbing boundaries, and examine how such boundary laws give rise to intrinsic information observables. Rather than introducing…
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting…
Atomic diffusion affects the properties of various engineering materials, which predominantly occur in the polycrystalline state. A rigorous description of polycrystalline diffusion must therefore account for crystallographic defects,…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
We derive an explicit formula for the fundamental solution $K_{T_{q+1}}(x,x_{0};t)$ to the discrete-time diffusion equation on the $(q+1)$-regular tree $T_{q+1}$ in terms of the discrete $I$-Bessel function. We then use the formula to…
Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However,…
This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…
We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely…
Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…