Path Integrals with Colored or Long-Range Noise

Develop path-integral formulations of generalized Langevin equations and related stochastic field-theoretic approaches that incorporate colored noise and long-range correlations, including fractional Lévy motion and fractional Brownian motion, rather than being restricted to Gaussian white noise.

Background

The discussion of generalized Langevin equations and extensions of stochastic path integrals highlights that current methods largely assume white noise. This limitation prevents modeling long-range temporal correlations and colored noise, which are central to anomalous diffusion and fractional processes.

By explicitly stating the challenge of incorporating colored or long-range correlated noise into path-integral frameworks, the paper identifies a concrete unresolved direction necessary for broader applicability of stochastic path integrals.

References

However, these methods are generally restricted to white noise processes, leaving open the challenge of incorporating colored noise or long-range correlations, such as those found in fractional Lévy or Brownian processes.

— Path Integral for Multiplicative Noise: Generalized Fokker-Planck Equation and Entropy Production Rate in Stochastic Processes With Threshold (2410.01387 - Abril-Bermúdez et al., 2 Oct 2024) in Section 1 (Introduction)