Related papers: Boundary Harnack Principle for Subordinate Brownia…
In this paper, we study small-time asymptotic behaviors for a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H\in(1/2,1)$ and magnitude $\ep^H$. By building up a…
In this paper we study the Martin boundary at infinity for a large class of purely discontinuous Feller processes on metric measure spaces. We show that if $\infty$ is accessible from an open set $D$, then there is only one Martin boundary…
Stiff forces, which bind objects together or otherwise confine motion, are found widely in soft-matter systems - colloids with short range attractions, ligand-receptor contacts, particles in optical traps, fibres that resist stretching,…
We present decay bounds for a broad class of Hermitian matrix functions where the matrix argument is banded or a Kronecker sum of banded matrices. Besides being significantly tighter than previous estimates, the new bounds closely capture…
We prove an uniform boundedness principle for the Lipschitz seminorm of continuous, monotone, positively homogeneous and subadditive mappings on suitable cones of functions. The result is applicable to several classes of classically…
We study some functional inequalities satisfied by the distribution of the solution of a stochastic differential equation driven by fractional Brownian motions. Such functional inequalities are obtained through new integration by parts…
In this work, a generalized Hopf's lemma and a global boundary Harnack inequality are proved for solutions to fractional $p$-Laplacian equations. Then, the isolation of the first $(s,p)$-eigenvalue is shown in bounded open sets satisfying…
We employ a variational approach to study the Neumann boundary value problem for the $p$-Laplacian on bounded smooth-enough domains in the metric setting, and show that solutions exist and are bounded. The boundary data considered are Borel…
We consider a class of stationary processes exhibiting both long-range dependence and heavy tails. Separate limit theorems for sums and for extremes have been established recently in literature with novel objects appearing in the limits. In…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
For a manifold with nonpositive curvature, the Martin boundary is described by the behavior of normalized Green's functions at infinity. A classical result by Anderson and Schoen states that if the manifold has pinched negative curvature,…
We construct Brownian motion on a wide class of metric spaces similar to graphs, and show that its cover time admits an upper bound depending only on the length of the space.
The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A…
In this paper we prove a uniform and scale invariant boundary Harnack principle at infinity for a large class of purely discontinuous Feller processes on metric measure spaces.
For $0<\alpha \leq 2$ and $0<H<1$, an $\alpha$-time fractional Brownian motion is an iterated process $Z = \{Z(t)=W(Y(t)), t \ge 0\}$ obtained by taking a fractional Brownian motion $\{W(t), t\in \RR{R} \}$ with Hurst index $0<H<1$ and…
Starting from an extension of the Poisson bracket structure and Kubo-Martin-Schwinger-property of classical statistical mechanics of continuous systems to spin systems, defined on a lattice, we derive a series of, as we think, new and…
We present a Korn-type inequality in a planar setting for special functions of bounded deformation. We prove that for each function in SBD$^2$ with sufficiently small jump set the distance of the function and its derivative from an…
A free non-relativistic particle moving in two dimensions on a half-plane can be described by self-adjoint Hamiltonians characterized by boundary conditions imposed on the systems. The most general boundary condition is parameterized in…
We consider the symmetric inclusion process on a general finite graph. Our main result establishes universal upper and lower bounds for the spectral gap of this interacting particle system in terms of the spectral gap of the random walk on…
We consider a stationary fluid queue with fractional Brownian motion input. Conditional on the workload at time zero being greater than a large value $b$, we provide the limiting distribution for the amount of time that the workload process…