1,414 research outputs found
Symmetric exclusion as a model of non-elliptic dynamical random conductances
We consider a finite range symmetric exclusion process on the integer lattice
in any dimension. We interpret it as a non-elliptic time-dependent random
conductance model by setting conductances equal to one over the edges with end
points occupied by particles of the exclusion process and to zero elsewhere. We
prove a law of large number and a central limit theorem for the random walk
driven by such a dynamical field of conductances by using the Kipnis-Varhadan
martingale approximation. Unlike the tagged particle in the exclusion process,
which is in some sense similar to this model, this random walk is diffusive
even in the one-dimensional nearest-neighbor case.Comment: Preliminary version, any comments are welcome. 9 page
Asymptotic variance of stationary reversible and normal Markov processes
We obtain necessary and sufficient conditions for the regular variation of
the variance of partial sums of functionals of discrete and continuous-time
stationary Markov processes with normal transition operators. We also construct
a class of Metropolis-Hastings algorithms which satisfy a central limit theorem
and invariance principle when the variance is not linear in
Central limit theorems for additive functionals of ergodic Markov diffusions processes
We revisit functional central limit theorems for additive functionals of
ergodic Markov diffusion processes. Translated in the language of partial
differential equations of evolution, they appear as diffusion limits in the
asymptotic analysis of Fokker-Planck type equations. We focus on the square
integrable framework, and we provide tractable conditions on the infinitesimal
generator, including degenerate or anomalously slow diffusions. We take
advantage on recent developments in the study of the trend to the equilibrium
of ergodic diffusions. We discuss examples and formulate open problems
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
Dirichlet forms methods, an application to the propagation of the error due to the Euler scheme
We present recent advances on Dirichlet forms methods either to extend
financial models beyond the usual stochastic calculus or to study stochastic
models with less classical tools. In this spirit, we interpret the asymptotic
error on the solution of an sde due to the Euler scheme in terms of a Dirichlet
form on the Wiener space, what allows to propagate this error thanks to
functional calculus.Comment: 15
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