112 research outputs found
On the zero mass limit of tagged particle diffusion in the 1-d Rayleigh-gas
We consider the M -> 0 limit for tagged particle diffusion in a 1-dimensional
Rayleigh-gas, studied originaly by Sinai and Soloveichik (1986), respectively
by Szasz and Toth (1986). In this limit we derive a new type of model for
tagged paricle diffusion, with Calogero-Moser-Sutherland (i.e. inverse
quadratic) interaction potential between the two central particles. Computer
simulations on this new model reproduce exactly the numerical value of the
limiting variance obtained by Boldrighini, Frigio and Tognetti (2002).Comment: Dedicated to Domokos Szasz on his 65th birthda
Continuous time `true' self-avoiding random walk on Z
We consider the continuous time version of the `true' or `myopic'
self-avoiding random walk with site repulsion in 1d. The Ray-Knight-type method
which was applied to the discrete time and edge repulsion case, is applicable
to this model with some modifications. We present a limit theorem for the local
time of the walk and a local limit theorem for the displacement.Comment: 17 page
Comment on a theorem of M. Maxwell and M. Woodroofe
We present a direct derivation of the theorem of M. Maxwell and M. Woodroofe
(Ann. Probab. 28 (2000) 713-724), on martingale approximation of additive
functionals of stationary Markov processes, from the non-reversible version of
the Kipnis-Varadhan theorem.Comment: revised version, to be published in Electronic Communications in
Probabilit
Relaxed sector condition
In this note we present a new sufficient condition which guarantees
martingale approximation and central limit theorem a la Kipnis-Varadhan to hold
for additive functionals of Markov processes. This condition which we call the
relaxed sector condition (RSC) generalizes the strong sector condition (SSC)
and the graded sector condition (GSC) in the case when the self-adjoint part of
the infinitesimal generator acts diagonally in the grading. The main advantage
being that the proof of the GSC in this case is more transparent and less
computational than in the original versions. We also hope that the RSC may have
direct applications where the earlier sector conditions don't apply. So far we
don't have convincing examples in this direction.Comment: 11 page
Modeling the Epps effect of cross correlations in asset prices
We review the decomposition method of stock return cross-correlations,
presented previously for studying the dependence of the correlation coefficient
on the resolution of data (Epps effect). Through a toy model of random
walk/Brownian motion and memoryless renewal process (i.e. Poisson point
process) of observation times we show that in case of analytical treatability,
by decomposing the correlations we get the exact result for the frequency
dependence. We also demonstrate that our approach produces reasonable fitting
of the dependence of correlations on the data resolution in case of empirical
data. Our results indicate that the Epps phenomenon is a product of the finite
time decay of lagged correlations of high resolution data, which does not scale
with activity. The characteristic time is due to a human time scale, the time
needed to react to news.Comment: to appear in the Proceedings of SPIE Fluctuations and Noise 200
Favourite sites of simple random walk
We survey the current status of the list of questions related to the
favourite (or: most visited) sites of simple random walk on Z, raised by Pal
Erdos and Pal Revesz in the early eighties.Comment: survey paper, 14 page
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