%0 Journal Article %1 bhattacharya1978criteria %A Bhattacharya, R. N. %D 1978 %I Institute of Mathematical Statistics %J The Annals of Probability %K PDE diffusions %N 4 %P pp. 541-553 %T Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions %U http://www.jstor.org/stable/2243121 %V 6 %X Let $L = 12 \sum^k_i,j=1 a_ij(x)(\partial^2/x_i x_j) + \sum^k_i=1 b_i(x)(\partial/x_i)$ 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{bhattacharya1978criteria, 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 $L$.}, added-at = {2011-10-31T05:50:28.000+0100}, author = {Bhattacharya, R. N.}, biburl = {https://www.bibsonomy.org/bibtex/29316e09179d0f4880972ee0e36c47769/peter.ralph}, copyright = {Copyright © 1978 Institute of Mathematical Statistics}, interhash = {009112e7be5048a5673b70122acaf751}, intrahash = {9316e09179d0f4880972ee0e36c47769}, issn = {00911798}, journal = {The Annals of Probability}, jstor_articletype = {research-article}, jstor_formatteddate = {Aug., 1978}, keywords = {PDE diffusions}, language = {English}, number = 4, pages = {pp. 541-553}, publisher = {Institute of Mathematical Statistics}, timestamp = {2011-10-31T05:50:28.000+0100}, title = {Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions}, url = {http://www.jstor.org/stable/2243121}, volume = 6, year = 1978 }