Related papers: Optimizing a variable-rate diffusion to hit an inf…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…
In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coeffcient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this…
This paper investigates a singular stochastic control problem for a multi-dimensional regime-switching diffusion process confined in an unbounded domain. The objective is to maximize the total expected discounted rewards from exerting the…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
In this article, we study the classical finite-horizon optimal stopping problem for multidimensional diffusions through an approach that differs from what is typically found in the literature. More specifically, we first prove a key…
This paper studies a two-material optimal design problem for the time-averaged duality pairing between a (possibly time-dependent) heat source and the weak solution of an initial-boundary value problem for the heat equation with a…
This paper is to investigate the control problem of maximizing the net benefit of a single species while the cost of the resource allocation is minimized in a population model which can be described by a reaction diffusion advection…
Preservation of the maximum principle is studied for the combination of the linear finite element method in space and the $\theta$-method in time for solving time dependent anisotropic diffusion problems. It is shown that the numerical…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
Consider the optimal stopping problem of a one-dimensional diffusion with positive discount. Based on Dynkin's characterization of the value as the minimal excessive majorant of the reward and considering its Riesz representation, we give…
The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
We investigate a class of diffusion-controlled reactions that are initiated at the time instance when a prescribed number $K$ among $N$ particles independently diffusing in a solvent are simultaneously bound to a target region. In the…
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
For an arbitrary diffusion process $X$ with time-homogeneous drift and variance parameters $\mu(x)$ and $\sigma^2(x)$, let $V_\varepsilon$ be $1/\varepsilon$ times the total time $X(t)$ spends in the strip…
We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…
This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional…
Diffusion with stochastic resetting, instantaneous returns of a diffusing particle to a reference point, creates a stationary probability distribution. The paradigm is extended here to a doubly stochastic protocol in which the resetting…