Refine
Document Type
- Article (1)
- Bachelor Thesis (1)
Language
- English (2)
Is part of the Bibliography
- yes (2)
Keywords
- autocorrelations (2) (remove)
Institute
Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc.
What remains less explored is the two time point correlation functions whose evaluation is often daunting since it requires the implementation of the exact time dependent probability density functions of the resetting processes which are unknown for most of the problems.
We adopt a different approach that allows us to write a stochastic solution for a single trajectory undergoing resetting.
Moments and the autocorrelation functions between any two times along the trajectory can then be computed directly using the laws of total expectation. Estimation of autocorrelation functions turns out to be pivotal for investigating the ergodic properties of various observables for this canonical model.
In particular, we investigate two observables (i) sample mean which is widely used in economics and (ii) time-averaged-mean-squared-displacement (TAMSD) which is of acute interest in physics.
We find that both diffusion and drift-diffusion processes with resetting are ergodic at the mean level unlike their reset-free counterparts. In contrast, resetting renders ergodicity breaking in the TAMSD while both the stochastic processes are ergodic when resetting is absent. We quantify these behaviors with detailed analytical study and corroborate with extensive numerical simulations.
Our results can be verified in experimental set-ups that can track single particle trajectories and thus have strong implications in understanding the physics of resetting.
Several authors highlighted that the time course of an experiment itself could have a substantial influence on the interpretability of experimental effects. Since mixed effects modeling had enabled researchers to investigate more complex problems with more precision than before, two naming experiments were conducted with college students, with and without non-words intermixed, and analyzed with regard to frequency, quality, interactive and trial-history effects. The present analyses build on and extend the Bates, Kliegl, Vasishth, and Baayen (2015) approach in order to converge on a parsimonious model that accounts for autocorrelated errors caused by trial history. For three of four cases, a history-sensitive model improved the model fit over a history-naïve model and explained more deviance. In one of these cases, the herein presented approach helped reveal an interaction between stimulus frequency and quality that was not significant without a trial history account. Main and joint effects, limitations, as well as directions for further research, are briefly discussed.