Delayed random walks

Delayed random walks.

Delayed Random Walks and Control

Issues of resonance that appear in non-standard random walk models are discussed. The first walk is called repulsive delayed random walk, which is described in the context of a stick balancing experiment. It will be shown that a type of ”resonant” effect takes place to keep the stability of the fixed point better with tuned bias and delay. We also briefly discuss the second model called sticky ...

Oscillatory correlation of delayed random walks

We investigate analytically and numerically the statistical properties of a random walk model with delayed transition probability dependence (delayed random walk). The characteristic feature of such a model is the oscillatory behavior of its correlation function. We investigate a model whose transient and stationary oscillatory behavior is analytically tractable. The correspondence of the model...

Spectral solution of delayed random walks.

We develop a spectral method for computing the probability density function for delayed random walks; for such problems, the method is exact to machine precision and faster than existing approaches. In conjunction with a step function approximation and the weak Euler-Maruyama discretization, the spectral method can be applied to nonlinear stochastic delay differential equations (SDDE). In essen...

Delayed random walks: Investigating the interplay between delay and noise

A model for a 1–dimensional delayed random walk is developed by generalizing the Ehrenfest model of a discrete random walk evolving on a quadratic, or harmonic, potential to the case of non–zero delay. The Fokker–Planck equation derived from this delayed random walk (DRW) is identical to that obtained starting from the delayed Langevin equation, i.e. a first–order stochastic delay differential ...