Increment sizes of the principal value of Brownian local time

2000 ◽  
Vol 117 (4) ◽  
pp. 515-531 ◽  
Author(s):  
Endre Csáki ◽  
Miklós Csörgő ◽  
Antónia Földes ◽  
Zhan Shi
Keyword(s):  
Local Time ◽  
Brownian Local Time ◽  
Principal Value

scholarly journals A CLT FOR THE THIRD INTEGRATED MOMENT OF BROWNIAN LOCAL TIME INCREMENTS

2011 ◽  
Vol 11 (01) ◽  
pp. 5-48
Author(s):  
JAY ROSEN
Keyword(s):  
Brownian Motion ◽  
Local Time ◽  
Random Variable ◽  
Normal Random Variable ◽  
Higher Moments ◽  
Second Moment ◽  
The Third ◽  
Brownian Local Time

Let [Formula: see text] denote the local time of Brownian motion. Our main result is to show that for each fixed t[Formula: see text] as h → 0, where η is a normal random variable with mean zero and variance one, that is independent of [Formula: see text]. This generalizes our previous result for the second moment. We also explain why our approach will not work for higher moments.

Hilbert transform of G-Brownian local time

2014 ◽  
Vol 14 (04) ◽  
pp. 1450006 ◽  
Author(s):  
Litan Yan ◽  
Qinghua Zhang ◽  
Bo Gao
Keyword(s):  
Brownian Motion ◽  
Local Time ◽  
Hilbert Transform ◽  
Natural Extension ◽  
Itô Integral ◽  
Brownian Local Time ◽  
Ito Integral ◽  
Natural Result ◽  
The Hilbert Transform

Let B be a G-Brownian motion with quadratic process 〈B〉 under the G-expectation. In this paper, we consider the integrals [Formula: see text] We show that the integral diverges and the convergence [Formula: see text] exists in 𝕃2 for all a ∈ ℝ, t > 0. This shows that [Formula: see text] coincides with the Hilbert transform of the local time [Formula: see text] of G-Brownian motion B for every t. The functional is a natural extension to classical cases. As a natural result we get a sublinear version of Yamada's formula [Formula: see text] where the integral is the Itô integral under the G-expectation.

scholarly journals Singularity of Super-Brownian Local Time at a Point Catalyst

1995 ◽  
Vol 23 (1) ◽  
pp. 37-55 ◽  
Author(s):  
Donald A. Dawson ◽  
Klaus Fleischmann ◽  
Yi Li ◽  
Carl Mueller
Keyword(s):  
Local Time ◽  
Brownian Local Time
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