Related papers: On optimal stopping of multidimensional diffusions
This work is motivated by the need to study the impact of data uncertainties and material imperfections on the solution to optimal control problems constrained by partial differential equations. We consider a pathwise optimal control…
Suppose that local characteristics of several independent compound Poisson and Wiener processes change suddenly and simultaneously at some unobservable disorder time. The problem is to detect the disorder time as quickly as possible after…
This article considers the problem of diffraction by a wedge consisting of two semi-infinite periodic arrays of point scatterers. The solution is obtained in terms of two coupled systems, each of which is solved using the discrete…
We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method…
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…
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…
In this paper, we study numerical methods for the solution of partial differential equations on evolving surfaces. The evolving hypersurface in $\Bbb{R}^d$ defines a $d$-dimensional space-time manifold in the space-time continuum…
We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial…
A weak Galerkin discretization of the boundary value problem of a general anisotropic diffusion problem is studied for preservation of the maximum principle. It is shown that the direct application of the $M$-matrix theory to the stiffness…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
We present a formulation of an optimal control problem for a two-dimensional diffusion process governed by a Fokker-Planck equation to achieve a nonequilibrium steady state with a desired circulation while accelerating convergence toward…
A general result on the method of randomized stopping is proved. It is applied to optimal stopping of controlled diffusion processes with unbounded coefficients to reduce it to an optimal control problem without stopping. This is motivated…
The purpose of this paper is to provide equations to model the evolution of effective diffusion over a Riemannian fiber bundle (under the hypothesis of infinite diffusion rate along compact fibers). These equations are obtained by…
This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization…
By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized problem has the same energy dissipation structure as the…
In this paper, we study a sampling problem where a source takes samples from a Wiener process and transmits them through a wireless channel to a remote estimator. Due to channel fading, interference, and potential collisions, the packet…
There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $\Omega \subset \R^d$ containing a set of small subdomains or interior…
We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria, weak equilibria and strong equilibria. The discount function is assumed to be log sub-additive and the…
Recent literature has effectively leveraged diffusion models trained on continuous variables as priors for solving inverse problems. Notably, discrete diffusion models with discrete latent codes have shown strong performance, particularly…
We establish a systematic solution method for optimal stopping problems of spectrally negative L\'evy processes. Our approach relies essentially on the potential theory, in particular the Riesz decomposition and the maximum principle. Using…