Abstract
For a L\'evy process $X_t$ with quadratic variation process $V_t=\sigma^2
t+ \sum_{00$, we give stability and compactness
results, as $t\downarrow 0$, for the convergence both of the deterministically
normed (and possibly centered) processes $X_t$ and $V_t$, as well as
theorems concerning the ``selfnormalised" process $X_{t}/\sqrt{V_t}$.
As a main application it is shown that $X_{t}/\sqrt{V_t}\Rightarrow N(0,1)$, a
standard normal random
variable, as $t\downarrow 0$, if and only if $X_t/b(t)\Rightarrow N(0,1)$, as $t\downarrow 0$,
for some nonstochastic function $b(t)>0$; thus, $X_t$ is in the domain of
attraction of the normal
distribution, as $t\downarrow 0$, with or without centering constants being
necessary (these being equivalent). We cite simple analytic equivalences
for the above properties, in terms of the L\'evy measure of $X$.
Information:
Date:  Tuesday, July 13, 2010, 9:0011:00  Place:  Niavaran Bldg., Niavaran Square, Tehran, Iran 
