The Annals of Probability

Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions

R. N. Bhattacharya

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Abstract

Let $L = \frac{1}{2} \sum^k_{i,j=1} a_{ij}(x)(\partial^2/\partial x_i \partial x_j) + \sum^k_{i=1} b_i(x)(\partial/\partial x_i)$ be an elliptic operator such that $a_{ij}(\bullet)$ are continuous and $b_i(\bullet)$ are measurable and bounded on compacts. Criteria for transience, null recurrence, and positive recurrence of diffusions on $R^k$ governed by $L$ are derived in terms of the coefficients of $L$.

Article information

Source
Ann. Probab., Volume 6, Number 4 (1978), 541-553.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995476

Digital Object Identifier
doi:10.1214/aop/1176995476

Mathematical Reviews number (MathSciNet)
MR494525

Zentralblatt MATH identifier
0386.60056

JSTOR
links.jstor.org

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

Keywords
$L$-harmonic functions strong Markov property invariant measures

Citation

Bhattacharya, R. N. Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions. Ann. Probab. 6 (1978), no. 4, 541--553. doi:10.1214/aop/1176995476. https://projecteuclid.org/euclid.aop/1176995476


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Corrections

  • See Correction: R. N. Bhattacharya. Correction Note: Correction to "Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions". Ann. Probab., Volume 8, Number 6 (1980), 1194--1195.