## The Annals of Probability

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

Jay Rosen

#### 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

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
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