@article{StojkoskiJolakoskiPaletal.2022,
  author    = {Stojkoski, Viktor and Jolakoski, Petar and Pal, Arnab and Sandev, Trifce and Kocarev, Ljupco and Metzler, Ralf},
  title     = {Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity},
  series = {Philosophical transactions of the Royal Society A: Mathematical, physical and engineering sciences},
  volume    = {380},
  journal   = {Philosophical transactions of the Royal Society A: Mathematical, physical and engineering sciences},
  number    = {2224},
  publisher = {Royal Society},
  address   = {London},
  issn      = {1364-503X},
  doi       = {10.1098/rsta.2021.0157},
  pages     = {17},
  year      = {2022},
  abstract  = {We explore the role of non-ergodicity in the relationship between income inequality, the extent of concentration in the income distribution, and income mobility, the feasibility of an individual to change their position in the income rankings. For this purpose, we use the properties of an established model for income growth that includes 'resetting' as a stabilizing force to ensure stationary dynamics. We find that the dynamics of inequality is regime-dependent: it may range from a strictly non-ergodic state where this phenomenon has an increasing trend, up to a stable regime where inequality is steady and the system efficiently mimics ergodicity. Mobility measures, conversely, are always stable over time, but suggest that economies become less mobile in non-ergodic regimes. By fitting the model to empirical data for the income share of the top earners in the USA, we provide evidence that the income dynamics in this country is consistently in a regime in which non-ergodicity characterizes inequality and immobility. Our results can serve as a simple rationale for the observed real-world income dynamics and as such aid in addressing non-ergodicity in various empirical settings across the globe.This article is part of the theme issue 'Kinetic exchange models of societies and economies'.},
  language  = {en}
}
@article{StojkoskiSandevKocarevetal.2022,
  author    = {Stojkoski, Viktor and Sandev, Trifce and Kocarev, Ljupco and Pal, Arnab},
  title     = {Autocorrelation functions and ergodicity in diffusion with stochastic resetting},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {55},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {10},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/ac4ce9},
  pages     = {22},
  year      = {2022},
  abstract  = {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.},
  language  = {en}
}