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We study a class of two-sided optimal control problems of general linear diffusions under a so-called Poisson constraint: the controlling is only allowed at the arrival times of an independent Poisson signal processes. We give a weak and…
We consider the effective surface motion of a particle that freely diffuses in the bulk and intermittently binds to that surface. From an exact approach we derive various regimes of the effective surface motion characterized by physical…
Diffusion processes arise in many fields, and so simulating the path of a diffusion is an important problem. It is usually necessary to make some sort of approximation via model-discretization, but a recently introduced class of algorithms,…
Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation…
We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…
The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time…
The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply and urban pollution. Motivated by this, we develop a large-deviation theory that…
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 study a model of non-interacting spinless fermions coupled to local dephasing and boundary drive and described within a Lindblad master equation. The model features an interplay between infinite temperature thermalization due to bulk…
Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal…
In this work, we consider the outer Stefan problem for the short-time prediction of the spread of a volatile asset traded in a financial market. The stochastic equation for the evolution of the density of sell and buy orders is the Heat…
A major obstacle for the understanding of long electrical discharges is the complex dynamics of streamer coronas, formed by many thin conducting filaments. Building macroscopic models for these filaments is one approach to attain a deeper…
We apply macroscopic fluctuation theory to study the diffusion of a tracer in a one-dimensional interacting particle system with excluded mutual passage, known as single-file diffusion. In the case of Brownian point particles with hard-core…
Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary…
The Brownian motion over the space of fluid velocity configurations driven by the hydrodynamical equations is considered. The Green function is computed in the form of an asymptotic series close to the standard diffusion kernel. The high…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
We consider a random model of diffusion and coagulation. A large number of small particles are randomly scattered at an initial time. Each particle has some integer mass and moves in a Brownian motion whose diffusion rate is determined by…
In this work we study a branching particle system of diffusion processes on the real line interacting through their rank in the system. Namely, each particle follows an independent Brownian motion, but only K $\ge$ 1 particles on the far…
We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…
The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the…