Related papers: Pathwise differentiability of reflected diffusions…
This work studies the parameter-dependent diffusion equation in a two-dimensional domain consisting of locally mirror symmetric layers. It is assumed that the diffusion coefficient is a constant in each layer. The goal is to find…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
We consider random flights in $\mathbb{R}^d$ reflecting on the surface of a sphere $\mathbb{S}^{d-1}_R,$ with center at the origin and with radius $R,$ where reflection is performed by means of circular inversion. Random flights studied in…
We prove the existence of the reflected diffusion on a complex of an arbitrary size for a large class of planar simple nested fractals. Such a process is obtained as a folding projection of the free Brownian motion from the unbounded…
This paper establishes the well-posedness of reflected backward stochastic differential equations in the non-convex domains that satisfy a weaker version of the star-shaped property. The main results are established (i) in a Markovian…
In this paper we first study the penalization approximation of stochastic differential equations reflected in a domain which satisfies conditions (A) and (B) and prove that the sequence of solutions of the penalizing equations converges in…
In this paper, we first review the penalization method for solving deterministic Skorokhod problems in non-convex domains and establish estimates for problems with $\alpha$-H\"older continuous functions. With the help of these results…
To characterize the Neumann problem for nonlinear Fokker-Planck equations, we investigate distribution dependent reflecting SDEs (DDRSDEs) in a domain. We first prove the well-posedness and establish functional inequalities for reflecting…
In order to characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine learning method to characterize…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
Reflected Brownian motion (RBM) in a convex polyhedral cone arises in a variety of applications ranging from the theory of stochastic networks to math finance, and under general stability conditions, it has a unique stationary distribution.…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
In this work, we introduce a new Skorokhod problem with two reflecting barriers when the trajectories of the driven process and the barriers are right and left limited. We show that this problem has an explicit unique solution in a…
The reflection and transmission amplitudes of waves in disordered multimode waveguides are studied by means of numerical simulations based on the invariant embedding equations. In particular, we analyze the influence of surface-type…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
This paper studies diffusion processes constrained to the positive orthant under infinitesimal changes in the drift. Our first main result states that any constrained function and its (left) drift-derivative is the unique solution to an…