scholarly journals Random walk local time approximated by a Brownian sheet combined with an independent Brownian motion

2009 ◽  
Vol 45 (2) ◽  
pp. 515-544 ◽  
Author(s):  
Endre Csáki ◽  
Miklós Csörgő ◽  
Antónia Földes ◽  
Pál Révész
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Local Time ◽  
Brownian Sheet ◽  
Independent Brownian Motion

Self-avoiding random walk: A Brownian motion model with local time drift

1987 ◽  
Vol 74 (2) ◽  
pp. 271-287 ◽  
Author(s):  
J. R. Norris ◽  
L. C. G. Rogers ◽  
David Williams
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Local Time ◽  
Motion Model ◽  
Time Drift ◽  
Brownian Motion Model

RENORMALISATION DU TEMPS LOCAL DES POINTS TRIPLES DU MOUVEMENT BROWNIEN

2006 ◽  
Vol 09 (04) ◽  
pp. 547-566 ◽  
Author(s):  
R. JENANE ◽  
R. HACHAICHI ◽  
L. STREIT
Keyword(s):  
Brownian Motion ◽  
Local Time ◽  
Wiener Integral ◽  
Intersection Local Time ◽  
Higher Dimensional ◽  
Independent Brownian Motion ◽  
Mouvement Brownien ◽  
Multiple Wiener Integral

We show that each term of the multiple Wiener integral expansion for the renormalized triple self-intersection local time of higher dimensional Brownien motion converges in law to an independent Brownian motion.

The Limit Distribution of level Crossings of a Random Walk, and a Simple Unit Root Test

1996 ◽  
Vol 12 (4) ◽  
pp. 705-723 ◽  
Author(s):  
Peter Burridge ◽  
Emmanuel Guerre
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Local Time ◽  
Limit Distribution ◽  
Unit Root ◽  
Unit Root Test ◽  
Level Crossings ◽  
Time Approximation

We derive the limit distribution of the number of crossings of a level by a random walk with continuously distributed increments, using a Brownian motion local time approximation. This complements the well-known result for the random walk on the integers. Use of the frequency of level crossings to test for a unit root is examined.

Limit distributions for the Bernoulli meander

1995 ◽  
Vol 32 (2) ◽  
pp. 375-395 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Limit Behavior ◽  
Explicit Formulas ◽  
Limit Distributions ◽  
Brownian Meander

This paper is concerned with the distibutions and the moments of the area and the local time of a random walk, called the Bernoulli meander. The limit behavior of the distributions and the moments is determined in the case where the number of steps in the random walk tends to infinity. The results of this paper yield explicit formulas for the distributions and the moments of the area and the local time for the Brownian meander.

scholarly journals On the local time of random walk on the 2-dimensional comb

2011 ◽  
Vol 121 (6) ◽  
pp. 1290-1314 ◽  
Author(s):  
Endre Csáki ◽  
Miklós Csörgő ◽  
Antónia Földes ◽  
Pál Révész
Keyword(s):  
Random Walk ◽  
Local Time

scholarly journals Thick points for planar Brownian motion and the Erdős-Taylor conjecture on random walk

2001 ◽  
Vol 186 (2) ◽  
pp. 239-270 ◽  
Author(s):  
Amir Dembo ◽  
Yuval Peres ◽  
Jay Rosen ◽  
Ofer Zeitouni
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Planar Brownian Motion ◽  
Thick Points
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