The Annals of Probability

A Mini-Max Variational Formula Giving Necessary and Sufficient Conditions for Recurrence or Transience of Multidimensional Diffusion Processes

Ross G. Pinsky

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Abstract

Let $L = \frac{1}{2} \nabla \cdot a\nabla + b \cdot \nabla$ generate a diffusion process on $R^d$. An expression involving $a$ and $b$ on $1 \leq |x| \leq n$ and two functions $g$ and $h$, varied over suitable domains, attains its mini-max value at $\lambda_n$. It is shown that $\lim_{n\rightarrow\infty}\lambda_n = 0$ or $\lim_{n\rightarrow\infty} \lambda_n > 0$ according to whether the process is recurrent or transient.

Article information

Source
Ann. Probab., Volume 16, Number 2 (1988), 662-671.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991779

Digital Object Identifier
doi:10.1214/aop/1176991779

Mathematical Reviews number (MathSciNet)
MR929069

Zentralblatt MATH identifier
0651.60079

JSTOR
links.jstor.org

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]

Keywords
Diffusion processes recurrence and transience mini-max variational formula

Citation

Pinsky, Ross G. A Mini-Max Variational Formula Giving Necessary and Sufficient Conditions for Recurrence or Transience of Multidimensional Diffusion Processes. Ann. Probab. 16 (1988), no. 2, 662--671. doi:10.1214/aop/1176991779. https://projecteuclid.org/euclid.aop/1176991779


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