Space representation of stochastic processes with delay.

  title={Space representation of stochastic processes with delay.},
  author={Silvio R. Dahmen and Haye Hinrichsen and Wolfgang Kinzel},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={77 3 Pt 1},
We show that a time series x(t) evolving by a nonlocal update rule x(t) =f (x(t-n),x(t-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… 
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