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Displaying similar documents to “Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited”

Wiener integral for the coordinate process under the σ-finite measure unifying brownian penalisations

Kouji Yano (2011)

ESAIM: Probability and Statistics

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Wiener integral for the coordinate process is defined under the -finite measure unifying Brownian penalisations, which has been introduced by [Najnudel , 345 (2007) 459–466] and [Najnudel , 19. Mathematical Society of Japan, Tokyo (2009)]. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study [K. Yano, 258 (2010) 3492–3516] of Cameron-Martin formula for the -finite measure.

Density of paths of iterated Lévy transforms of brownian motion

Marc Malric (2012)

ESAIM: Probability and Statistics

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The Lévy transform of a Brownian motion is the Brownian motion given by = sgn()d; call the Brownian motion obtained from by iterating times this transformation. We establish that almost surely, the sequence of paths ( → ) is dense in Wiener space, for the topology of uniform convergence on compact time intervals.

Density of paths of iterated Lévy transforms of Brownian motion

Marc Malric (2012)

ESAIM: Probability and Statistics

Similarity:

The Lévy transform of a Brownian motion is the Brownian motion given by = sgn()d; call the Brownian motion obtained from by iterating times this transformation. We establish that almost surely, the sequence of paths ( → ) is dense in Wiener space, for the topology of uniform...

α-time fractional Brownian motion: PDE connections and local times

Erkan Nane, Dongsheng Wu, Yimin Xiao (2012)

ESAIM: Probability and Statistics

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For 0 <  ≤ 2 and 0 <  < 1, an -time fractional Brownian motion is an iterated process  =  {() = (()) ≥ 0}  obtained by taking a fractional Brownian motion  {() ∈ ℝ} with Hurst index 0 <  < 1 and replacing the time parameter with a strictly -stable Lévy process {() ≥ 0} in ℝ independent of {() ∈ R}. It is shown that such processes have natural connections to partial differential equations and, when ...

α-time fractional brownian motion: PDE connections and local times

Erkan Nane, Dongsheng Wu, Yimin Xiao (2012)

ESAIM: Probability and Statistics

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For 0 &lt;  ≤ 2 and 0 &lt;  &lt; 1, an -time fractional Brownian motion is an iterated process  =  {() = (()) ≥ 0}  obtained by taking a fractional Brownian motion  {() ∈ ℝ} with Hurst index 0 &lt;  &lt; 1 and replacing the time parameter with a strictly -stable Lévy process {() ≥ 0} in ℝ independent of {() ∈ R}. It is shown that such processes have natural connections to partial differential equations and, when is a stable subordinator, can arise as scaling limit...

Universality of slow decorrelation in KPZ growth

Ivan Corwin, Patrik L. Ferrari, Sandrine Péché (2012)

Annales de l'I.H.P. Probabilités et statistiques

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There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar–Parisi–Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting fluctuations. In one-dimension, the KPZ class has the dynamical scaling exponent = 3/2, that means one should find a universal space–time limiting process under the scaling of time as , space like 2/3 and fluctuations like 1/3 as → ∞. In this paper...