Stochastic dynamics with multiplicative dichotomic noise: Heterogeneous telegrapher’s equation, anomalous crossovers and resetting

We analyze diffusion processes with finite propagation speed in a non-homogeneous medium terms of the heterogeneous telegrapher’s equation. In limit infinite-velocity we recover results for process. The process exhibits rich variety regimes including hyperdiffusion, ballistic motion, superdiffusion, normal and subdiffusion, different crossover dynamics characteristic complex systems which anomalous is observed. exponent short time twice long limit, accordance to from standard also finite-velocity presence stochastic Poissonian resetting. show that system reaches non-equilibrium stationary state. transition this steady state analyzed large deviation function.