Related papers: An algorithm to solve optimal stopping problems fo…
We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
In the paper "Dynkin Games Via Dirichlet Forms and Singular Control of One-Dimensional Diffusion", the authors tried to show the existences of a smooth value function and an optimal policy to a one-dimensional stochastic singular control…
Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for…
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 study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is…
In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on…
We study the value and the optimal strategies for a two-player zero-sum optimal stopping game with incomplete and asymmetric information. In our Bayesian set-up, the drift of the underlying diffusion process is unknown to one player…
We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations…
In this paper, we consider the problem of jointly performing online parameter estimation and optimal sensor placement for a partially observed infinite dimensional linear diffusion process. We present a novel solution to this problem in the…
Diffusion inversion aims to recover the initial noise corresponding to a given image such that this noise can reconstruct the original image through the denoising diffusion process. The key component of diffusion inversion is to minimize…
Diffusion models excel at capturing complex data distributions, such as those of natural images and proteins. While diffusion models are trained to represent the distribution in the training dataset, we often are more concerned with other…
Diffusion-induced Ramsey narrowing that appears when atoms can leave the interaction region and repeatedly return without lost of coherence is investigated using strong collisions approximation. The effective diffusion equation is obtained…
This paper is concerned with the construction of a fast algorithm for computing the maximum speed of propagation in the Riemann solution for the Euler system of gas dynamics with the co-volume equation of state. The novelty in the algorithm…
In this article we consider the ergodic risk-sensitive control problem for a large class of multidimensional controlled diffusions on the whole space. We study the minimization and maximization problems under either a blanket stability…
Diffusion models have achieved remarkable success in generative modeling. Despite more stable training, the loss of diffusion models is not indicative of absolute data-fitting quality, since its optimal value is typically not zero but…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed,…
We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of a passive scalar (e.g., the concentration of a pollutant).…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…