The Annals of Probability

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

Jay Rosen

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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


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