Stochastic processes with stable distributions in random environments

The asymptotic behavior in random environments of random flights with stable distribution laws is analyzed by the field-theoretic renormalization group. Random force fields with isotropic, divergenceless, curl-free, and unconstrained pair correlation functions with both finite and infinite correlation length are considered. Stability of the effective distribution laws in the scaling limit is determined and the scaling dimension of time is calculated in the {ε}=dc-d expansion, where dc is the critical dimension of the model. {} 1996 The American Physical Society.