Space Representation of Stochastic Processes with Delay

الأصل · EN

We show that a time series xₜ evolving by a non-local 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 non-equilibrium 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 directed percolation.