Space representation of stochastic processes with delay
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Date
2008Type
Abstract
We show that a time series xt evolving by a nonlocal update rule xt= f (xt−n ,xt−k) with two different delays k<n can be mapped onto a local process in two dimensions with special time-delayed boundary conditions, provided that n and k are coprime. For certain stochastic update rules exhibiting a nonequilibrium phase transition, this mapping implies that the critical behavior does not depend on the short delay k. In these cases, the autocorrelation function of the time series is related to the ...
We show that a time series xt evolving by a nonlocal update rule xt= f (xt−n ,xt−k) with two different delays k<n can be mapped onto a local process in two dimensions with special time-delayed boundary conditions, provided that n and k are coprime. For certain stochastic update rules exhibiting a nonequilibrium phase transition, this mapping implies that the critical behavior does not depend on the short delay k. In these cases, the autocorrelation function of the time series is related to the critical properties of the corresponding twodimensional model. ...
In
Physical review. E, Statistical, nonlinear, and soft matter physics. Vol. 77, no. 3 (Mar. 2008), 031106, 6 p.
Source
Foreign
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