# Scaled Brownian motion with renewal resetting

## TL;DR

This paper studies a stochastic process combining scaled Brownian motion with stochastic resetting, focusing on how memory erasure at reset affects probability densities and first passage properties, with implications for search efficiency.

## Contribution

It introduces a fully renewal model of scaled Brownian motion with resetting, analyzing how memory erasure influences process properties and search efficiency.

## Key findings

- Memory erasure significantly alters probability density functions.
- First passage times are affected by the renewal resetting mechanism.
- Search efficiency depends on process parameters and memory effects.

## Abstract

We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient $D(t) \sim t^{\alpha -1}$ with $\alpha > 0$ (scaled Brownian motion) is stochastically reset to its initial position, and starts anew. \color{black} 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 coordinate does not affect the diffusion coefficient's time dependence is considered in the other work of this series. We show that the properties of the probability densities in such processes (erazing or retaining the memory on the diffusion coefficient) are vastly different. \color{black} 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.