scholarly journals On transient Bessel processes and planar Brownian motion reflected at their future infima

1995 ◽  
Vol 60 (1) ◽  
pp. 87-102 ◽  
Author(s):  
Z. Shi
Keyword(s):  
Brownian Motion ◽  
Bessel Processes ◽  
Planar Brownian Motion

scholarly journals Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Satya N. Majumdar ◽  
Francesco Mori ◽  
Hendrik Schawe ◽  
Grégory Schehr
Keyword(s):  
Brownian Motion ◽  
Convex Hull ◽  
Planar Brownian Motion

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

Systèmes dynamiques gaussiens d'entropie nulle, lâchement et non lâchement Bernoulli

1996 ◽  
Vol 16 (2) ◽  
pp. 379-404 ◽  
Author(s):  
Thierry De La Rue
Keyword(s):  
Brownian Motion ◽  
Dynamical Systems ◽  
Planar Brownian Motion ◽  
Zero Entropy

AbstractWe construct two real Gaussian dynamical systems of zero entropy; the first one is not loosely Bernoulli, and the second is a loosely Bernoulli Gaussian-Kronecker system. To get loose-Bernoullicity for the second system, we prove and use a property of planar Brownian motion on [0, 1]: we can recover the whole trajectory knowing only some angles formed by the motion.

scholarly journals Occupation Times, Drawdowns, and Drawups for One-Dimensional Regular Diffusions

2015 ◽  
Vol 47 (1) ◽  
pp. 210-230 ◽  
Author(s):  
Hongzhong Zhang
Keyword(s):  
Brownian Motion ◽  
Diffusion Process ◽  
Time Horizon ◽  
Three Dimensional ◽  
Bessel Processes ◽  
Occupation Times ◽  
Exponential Time ◽  
One Dimensional ◽  
Brownian Motion With Drift ◽  
Running Maximum

The drawdown process of a one-dimensional regular diffusion process X is given by X reflected at its running maximum. The drawup process is given by X reflected at its running minimum. We calculate the probability that a drawdown precedes a drawup in an exponential time-horizon. We then study the law of the occupation times of the drawdown process and the drawup process. These results are applied to address problems in risk analysis and for option pricing of the drawdown process. Finally, we present examples of Brownian motion with drift and three-dimensional Bessel processes, where we prove an identity in law.

scholarly journals Anyonic partition functions and windings of planar Brownian motion

1995 ◽  
Vol 51 (2) ◽  
pp. 942-945 ◽  
Author(s):  
Jean Desbois ◽  
Christine Heinemann ◽  
Stéphane Ouvry
Keyword(s):  
Brownian Motion ◽  
Partition Functions ◽  
Planar Brownian Motion
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