Related papers: Bounded Bessel Processes and Ferrari-Spohn Diffusi…
The Ferrari-Spohn diffusion process arises as limit process for the 2D Ising model as well as random walks with area penalty. Motivated by the 3D Ising model, we consider $M$ such diffusions conditioned not to intersect. We show that the…
The squared Bessel process is a 1-dimensional diffusion process related to the squared norm of a higher dimensional Brownian motion. We study a model of $n$ non-intersecting squared Bessel paths, with all paths starting at the same point…
The present paper is concerned with diffusion processes running on tubular domains with conditions on nonreaching the boundary, respectively, reflecting at the boundary, and corresponding processes in the limit where the thin tubular…
We establish a process level large deviation principle for systems of interacting Bessel-like diffusion processes. By establishing weak uniqueness for the limiting non-local SDE of McKean-Vlasov type, we conclude that the latter describes…
We consider families of non-colliding random walks above a hard wall, which are subject to a self-potential of tilted area type. We view such ensembles as effective models for the level lines of a class of $2+1$-dimensional discrete-height…
Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those diffusions, the…
We provide, in a general setting, explicit solutions for optimal stopping problems that involve a diffusion process and its running maximum. Besides, a new feature includes absorbing boundaries that vary with the value of the running…
Ram\'irez and Rider (2009) established that the hard edge of the spectrum of the $\beta$-Laguerre ensemble converges, in the high-dimensional limit, to the bottom of the spectrum of the stochastic Bessel operator. Using stochastic analysis…
We prove an invariance principle for a class of tilted (1+1)-dimensional SOS models or, equivalently, for a class of tilted random walk bridges in Z_+. The limiting objects are stationary reversible ergodic diffusions with drifts given by…
In this article we prove the existence of Bernstein processes which we associate in a natural way with a class of linear parabolic initial-and final boundary value problems defined in bounded convex subsets of Euclidean space of arbitrary…
I consider a stochastic optimization problem for a time-changed Bessel process whose diffusion rate is constrained to be between two positive values $r_{1}<r_{2}$. The problem is to find an optimal adapted strategy for the choice of…
In this paper, we investigate the construction of a diffusion process whose time-marginal densities are constrained to belong to a given set at all time. The construction is obtained from a penalization approximation to the constraint set,…
We investigate, through simulation, the modifications to Bessel and Airy beams during propagation through atmospheric turbulence. We find that atmospheric turbulence disrupts the quasi-non-diffracting nature of Bessel and Airy beams when…
A system of non-intersecting squared Bessel processes is considered which all start from one point and they all return to another point. Under the scaling of the starting and ending points when the macroscopic boundary of the paths touches…
We consider the Dyson Ferrari--Spohn diffusion $\mathcal{X}^N = (\mathcal{X}^N_1,\dots,\mathcal{X}^N_N)$, consisting of $N$ non-intersecting Ferrari--Spohn diffusions $\mathcal{X}^N_1 > \cdots > \mathcal{X}^N_N > 0$ on $\mathbb{R}$. This…
The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusions processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially…
This paper is concerned with the large-time behavior of solutions to the Cauchy problem on the two-fluid Euler-Maxwell system with collisions when initial data are around a constant equilibrium state. The main goal is the rigorous…
We suggest a rigorous definition of the pathwise flux across the boundary of a bounded open set for transient finite energy diffusion processes. The expectation of such a flux has the property of depending only on the current velocity $v$,…
In this paper we consider diffusions on the half line (0, $\infty$) such that the expectation of the arrival time at the origin is uniformly bounded in the initial point. This implies that there is a well defined diffusion process starting…
We study the Poisson equation Lu+f=0 in R^d, where L is the infinitesimal generator of a diffusion process. In this paper, we allow the second-order part of the generator L to be degenerate, provided a local condition of Doeblin type is…