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August, 1978 Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions
R. N. Bhattacharya
Ann. Probab. 6(4): 541-553 (August, 1978). DOI: 10.1214/aop/1176995476

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 $L$.

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R. N. Bhattacharya. "Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions." Ann. Probab. 6 (4) 541 - 553, August, 1978. https://doi.org/10.1214/aop/1176995476

Information

Published: August, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0386.60056
MathSciNet: MR494525
Digital Object Identifier: 10.1214/aop/1176995476

Subjects:
Primary: 60J60

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 4 • August, 1978
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