Scaled Brownian motion with renewal resetting

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2019. Vol. 100. No. 1. P. 012120-1–012120-13.

Bodrova A., Chechkin A., Sokolov I.

We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion
coefficient D(t ) ∼ t α−1 with α > 0 (scaled Brownian motion) is stochastically reset to its initial position, and
starts anew. In the present work we discuss the situation in which the memory on the value of the diffusion
coefficient at a resetting time is erased, so that the whole process is a fully renewal one. The situation when
the resetting of the coordinate does not affect the diffusion coefficient’s time dependence is considered in the
other work of this series [A. S. Bodrova et al., Phys. Rev. E 100, 012119 (2019)]. We show that the properties
of the probability densities in such processes (erasing or retaining the memory on the diffusion coefficient) are
vastly different. In addition we discuss the first-passage properties of the scaled Brownian motion with renewal
resetting and consider the dependence of the efficiency of search on the parameters of the process.

Keywords: anomalous diffusion, аномальная диффузия