Kinetic equation of linear fractional stable motion and applications to modeling the scaling of intermittent bursts

first_imgLévy flights and fractional Brownian motion have become exemplars of the heavy-tailed jumps and longrangedmemory widely seen in physics. Natural time series frequently combine both effects, and linear fractionalstable motion lfsm is a model process of this type, combining alpha-stable jumps with a memory kernel.In contrast complex physical spatiotemporal diffusion processes where both the above effects compete have formany years been modeled using the fully fractional kinetic equation for the continuous-time random walkCTRW, with power laws in the probability density functions of both jump size and waiting time. We derivethe analogous kinetic equation for lfsm and show that it has a diffusion coefficient with a power law in timerather than having a fractional time derivative like the CTRW. We discuss some preliminary results on thescaling of burst “sizes” and “durations” in lfsm time series, with applications to modeling existing observationsin space physics and elsewhere.last_img read more