scholarly journals Scaling limits of random processes and the outer boundary of Planar Brownian motion

2000 ◽  
Vol 2000 (1) ◽  
pp. 233-253
Author(s):  
Oded Schramm
Keyword(s):  
Brownian Motion ◽  
Outer Boundary ◽  
Random Processes ◽  
Scaling Limits ◽  
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.

Sample quantiles of additive renewal reward processes

1996 ◽  
Vol 33 (04) ◽  
pp. 1018-1032 ◽  
Author(s):  
Angelos Dassios
Keyword(s):  
Brownian Motion ◽  
Random Processes ◽  
Independent Increments ◽  
Look Back ◽  
Renewal Reward Processes ◽  
Reward Process ◽  
Renewal Reward Process ◽  
Sample Quantiles

The distribution of the sample quantiles of random processes is important for the pricing of some of the so-called financial ‘look-back' options. In this paper a representation of the distribution of the α-quantile of an additive renewal reward process is obtained as the sum of the supremum and the infimum of two rescaled independent copies of the process. This representation has already been proved for processes with stationary and independent increments. As an example, the distribution of the α-quantile of a randomly observed Brownian motion is obtained.

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

scholarly journals Multiple Intersection Exponents for Planar Brownian Motion

2009 ◽  
Vol 136 (2) ◽  
pp. 373-397
Author(s):  
Achim Klenke ◽  
Peter Mörters
Keyword(s):  
Brownian Motion ◽  
Planar Brownian Motion

scholarly journals Polymer measure: Varadhan's renormalization revisited

2015 ◽  
Vol 27 (03) ◽  
pp. 1550009 ◽  
Author(s):  
Wolfgang Bock ◽  
Maria João Oliveira ◽  
José Luís da Silva ◽  
Ludwig Streit
Keyword(s):  
Brownian Motion ◽  
Rate Of Convergence ◽  
Local Time ◽  
Intersection Local Time ◽  
Planar Brownian Motion ◽  
Chaos Decomposition

Through chaos decomposition, we improve the Varadhan estimate for the rate of convergence of the centered approximate self-intersection local time of planar Brownian motion.

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