相关论文: A boundary Harnack principle and its application t…

In this paper, a necessary and sufficient condition is obtained for the scale invariant boundary Harnack inequality (BHP in abbreviation) for a large class of Hunt processes on metric measure spaces that are in weak duality with another…

We establish a boundary Harnack principle for a large class of subordinate Brownian motion, including mixtures of symmetric stable processes, in bounded $\kappa$-fat open set (disconnected analogue of John domains). As an application of the…

This paper gives an accessible (but still technical) self-contained proof to the fact that the intersection probabilities for planar Brownian motion are given in terms of the intersection exponents, up to a bounded multiplicative error, and…

We prove the Harnack inequality and boundary Harnack principle for the absolute value of a one-dimensional recurrent subordinate Brownian motion killed upon hitting $0$, when $0$ is regular for itself and the Laplace exponent of the…

For $d\geq 1$ and $\alpha \in (0, 2)$, consider the family of pseudo differential operators $\{\Delta+ b \Delta^{\alpha/2}; b\in [0, 1]\}$ on $\R^d$ that evolves continuously from $\Delta$ to $\Delta + \Delta^{\alpha/2}$. In this paper, we…

We show that the intersection exponents for planar Brownian motions are analytic. More precisely, let $B$ and $B'$ be independent planar Brownian motions started from distinct points, and define the exponent $\xi (1, \lambda)$ by $$…

We prove a generalized version of the $3G$ Principle for Green's functions on bounded inner uniform domains in a wide class of Dirichlet spaces. In particular, our results apply to higher-dimensional fractals such as Sierpinski carpets in…

We investigate the Boundary Harnack Principle in H\"older domains of exponent $\alpha>0$ by the analytical method developed in our previous work "A short proof of Boundary Harnack Principle".

We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic…

In this paper, we consider a large class of subordinate Brownian motions $X$ via subordinators with Laplace exponents which are complete Bernstein functions satisfying some mild scaling conditions at zero and at infinity. We first discuss…

In this paper we study the Martin boundary of unbounded open sets at infinity for a large class of subordinate Brownian motions. We first prove that, for such subordinate Brownian motions, the uniform boundary Harnack principle at infinity…

We study boundary inference at $H=3/4$ for mixed fractional Brownian motion and mixed fractional Ornstein--Uhlenbeck models under high-frequency observation. This boundary is economically important because it separates the critical and…

Let $Z$ be a subordinate Brownian motion in ${\mathbb R}^d$, $d\ge 2$, via a subordinator with Laplace exponent $\phi$. We kill the process $Z$ upon exiting a bounded open set $D\subset {\mathbb R}^d$ to obtain the killed process $Z^D$, and…

Starting from the hyperbolic Brownian motion as a time-changed Brownian motion, we explore a set of probabilistic models--related to the SABR model in mathematical finance--which can be obtained by geometry-preserving transformations, and…

We present a proof of scale-invariant boundary Harnack principle for uniform domains when the underlying space satisfies a scale-invariant elliptic Harnack inequality. Our approach does not assume the underlying space to be geodesic.…

Consider the intersection measure $\ell^{\mathrm{IS}}_t$ of $p$ independent Brownian motions on $\mathbb{R}^d$. In this article, we prove the large deviation principle for the normalized intersection measure $t^{-p}\ell^{\mathrm{IS}}_t$ as…

We establish a C^1,alpha Schauder estimate of a non-standard degenerate elliptic equation and use it to give another proof of the higher order boundary Harnack inequality. As an application, we obtain the analyticity of the free boundary in…

Let $\{B_{t}\}_{t\geq0}$ be a fractional Brownian motion with Hurst parameter $\frac{2}{3}<H<1$. We prove that the approximation of the derivative of self-intersection local time, defined as \begin{align*} \alpha_{\varepsilon} &=…

We prove that minimal graphs (other than planes) are parabolic in the sense that any bounded harmonic function is determined by its boundary values. The proof relies on using the coupling introduced in the author's earlier paper "A…

We consider pairs of 3-dimensional Brownian paths, started at the origin and conditioned to have no intersections after time zero. We show that there exists a unique measure on pairs of paths that is invariant under this conditioning, while…