## The Annals of Probability

- Ann. Probab.
- Volume 16, Number 1 (1988), 75-79.

### Continuity and Singularity of the Intersection Local Time of Stable Processes in $\mathbb{R}^2$

#### Abstract

We show that the planar symmetric stable process $X_t$ of index $\frac{4}{3} < \beta < 2$ has an intersection local time $\alpha(x, \cdot)$ which is weakly continuous in $x \neq 0$, while $\alpha(x, \lbrack 0, T\rbrack^2) \sim \frac{c}{|x|^{2 - \beta}}, \quad\text{as} x \rightarrow 0.$

#### Article information

**Source**

Ann. Probab., Volume 16, Number 1 (1988), 75-79.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176991886

**Digital Object Identifier**

doi:10.1214/aop/1176991886

**Mathematical Reviews number (MathSciNet)**

MR920256

**Zentralblatt MATH identifier**

0644.60078

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60J55: Local time and additive functionals

Secondary: 60J25: Continuous-time Markov processes on general state spaces

**Keywords**

Intersection local time stable processes

#### Citation

Rosen, Jay. Continuity and Singularity of the Intersection Local Time of Stable Processes in $\mathbb{R}^2$. Ann. Probab. 16 (1988), no. 1, 75--79. doi:10.1214/aop/1176991886. https://projecteuclid.org/euclid.aop/1176991886