Quelques approximations du temps local brownien

Details Quelques approximations du temps local brownien Quelques approximations du temps local brownien

2006-09-25

arxiv.org/abs/math/0609701v3

Mathematics

Probability

Soumis dans les Comptes rendus - Math\'ematique

Scientific paper

We give some approximations of the local time process $(L_t^x)_{t\geqslant 0}$ at level $x$ of the real Brownian motion $(X_t)$. We prove that $ \frac{2}{\epsilon}\int_0^{t} X_{(u+\epsilon)\wedge t}^+ \indi_{\{X_u \leqslant 0\}} du + \frac{2}{\epsilon}\int_0^{t} X_{(u+\epsilon) \wedge t}^- \indi_{\{X_u>0\}} du$ and $\frac{4}{\epsilon}\int_0^{t} X_u^- \indi_{\{X_{(u+\epsilon) \wedge t} > 0\}} du$ converge in the ucp sense to $L_t^0$, as $\epsilon \to 0$. We show that $ \frac{1}{\epsilon}\int_0^t (\indi_{\{x

Affiliated with

Also associated with

No associations

Rating

Quelques approximations du temps local brownien does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quelques approximations du temps local brownien, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quelques approximations du temps local brownien will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-15697