A Mini-Max Variational Formula Giving Necessary and Sufficient Conditions for Recurrence or Transience of Multidimensional Diffusion Processes
Pinsky, Ross G.
Ann. Probab., Tome 16 (1988) no. 4, p. 662-671 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 1988-04-14
Classification:  Diffusion processes,  recurrence and transience,  mini-max variational formula,  60J60 
@article{1176991779,
     author = {Pinsky, Ross G.},
     title = {A Mini-Max Variational Formula Giving Necessary and Sufficient Conditions for Recurrence or Transience of Multidimensional Diffusion Processes},
     journal = {Ann. Probab.},
     volume = {16},
     number = {4},
     year = {1988},
     pages = { 662-671},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991779}
}

Pinsky, Ross G. A Mini-Max Variational Formula Giving Necessary and Sufficient Conditions for Recurrence or Transience of Multidimensional Diffusion Processes. Ann. Probab., Tome 16 (1988) no. 4, pp.  662-671. http://gdmltest.u-ga.fr/item/1176991779/