Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions
Bhattacharya, R. N.
Ann. Probab., Tome 6 (1978) no. 6, p. 541-553 / Harvested from Project Euclid
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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 $L$.
Publié le : 1978-08-14
Classification:  $L$-harmonic functions,  strong Markov property,  invariant measures,  60J60 
@article{1176995476,
     author = {Bhattacharya, R. N.},
     title = {Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions},
     journal = {Ann. Probab.},
     volume = {6},
     number = {6},
     year = {1978},
     pages = { 541-553},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995476}
}

Bhattacharya, R. N. Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions. Ann. Probab., Tome 6 (1978) no. 6, pp.  541-553. http://gdmltest.u-ga.fr/item/1176995476/