The Size of an Analytic Function as Measured by Levy's Time Change
McConnell, Terry R.
Ann. Probab., Tome 13 (1985) no. 4, p. 1003-1005 / Harvested from Project Euclid
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For $f$ analytic in the unit disc put $\nu(f) = \int^\tau_0 |f'(B(s))|^2 ds$ where $\tau$ is the exit time of Brownian motion $B(t)$ from the disc. We prove that $E\Phi(\tau) \leq E\Phi(\nu(f))$ for all $f$ satisfying $|f'(0)| = 1$ and a wide class of $\Phi$. In particular, we may take $\Phi(\lambda) = |\lambda|^P$ for $0 < p < \infty$.
Publié le : 1985-08-14
Classification:  Analytic functions,  Brownian motion,  60J65,  30A42 
@article{1176992921,
     author = {McConnell, Terry R.},
     title = {The Size of an Analytic Function as Measured by Levy's Time Change},
     journal = {Ann. Probab.},
     volume = {13},
     number = {4},
     year = {1985},
     pages = { 1003-1005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992921}
}

McConnell, Terry R. The Size of an Analytic Function as Measured by Levy's Time Change. Ann. Probab., Tome 13 (1985) no. 4, pp.  1003-1005. http://gdmltest.u-ga.fr/item/1176992921/