Nonergodicity of reset geometric Brownian motion.

We derive. the ensemble- and time-averaged mean-squared displacements (MSD, TAMSD) for Poisson-reset geometric Brownian motion (GBM), in agreement with simulations. We find MSD and TAMSD saturation for frequent resetting, quantify the spread of TAMSDs via the ergodicity-breaking parameter and compute distributions of prices. General MSD-TAMSD nonequivalence proves reset GBM nonergodic.

• Publication year

  2022

• Venue

  Physical Review E

• Publication date

  2022-01-01

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1103/physreve.105.l012106PMID 35193263
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

  2021cited by this paper
• Scaled geometric Brownian motion features sub- or superexponential ensemble-averaged, but linear time-averaged mean-squared displacements.

  2021cited by this paper
• Anomalous diffusion, nonergodicity, and ageing for exponentially and logarithmically time-dependent diffusivity: striking differences for massive versus massless particles

  2021cited by this paper
• Geometric Brownian motion under stochastic resetting: A stationary yet nonergodic process.

  2021cited by this paper
• Fat tails and black swans: Exact results for multiplicative processes with resets.

  2020cited by this paper
• Stochastic resetting and applications

  2019cited by this paper
• The ergodicity problem in economics

  2019cited by this paper
• Nonrenewal resetting of scaled Brownian motion.

  2018cited by this paper
• Time averages and their statistical variation for the Ornstein-Uhlenbeck process: Role of initial particle distributions and relaxation to stationarity.

  2018cited by this paper
• Spectral content of fractional Brownian motion with stochastic reset

  2018cited by this paper
• Time averaging, ageing and delay analysis of financial time series

  2017cited by this paper
• Directed random walk with random restarts: The Sisyphus random walk.

  2016cited by this paper
• Dynamics of inequality

  2016cited by this paper
• Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking.

  2014cited by this paper
• Ergodicity breaking in geometric Brownian motion.

  2012cited by this paper
• Diffusion with stochastic resetting.

  2011cited by this paper
• Ito, Stratonovich, Hänggi and all the rest: The thermodynamics of interpretation

  2010cited by this paper
• Lookback options and diffusion hitting times: A spectral expansion approach

  2004cited by this paper
• Pricing and Hedging Path-Dependent Options Under the CEV Process

  2001cited by this paper
• The Analytics of Reset Options

  2000cited by this paper
• Reset Put Options: Valuation, Risk Characteristics, and an Application

  1999cited by this paper
• Pricing Lookback and Barrier Options under the CEV Process

  1999cited by this paper
• Stochastic multiplicative processes with reset events.

  1999cited by this paper
• Double Lookbacks

  1998cited by this paper
• Innovations: Valuing S&P 500 Bear Market Warrants with a Periodic Reset

  1997cited by this paper
• Path Dependent Options: The Case of Lookback Options

  1991cited by this paper
• Path Dependent Options: "Buy at the Low, Sell at the High"

  1979cited by this paper

• Shear-driven finite-velocity diffusion and its generalization.

  2026cites this paper
• Mass separation of brownian particles via multi-parameter dynamic regulation

  2025cites this paper
• On the Motion of a Charged Colloid with a Harmonic Trap

  2025cites this paper
• Steering chiral active Brownian motion via stochastic position-orientation resetting

  2025cites this paper
• Pairwise correlations of global times in one-dimensional Brownian motion under stochastic resetting.

  2025cites this paper
• Master equations for continuous-time random walks with stochastic resetting

  2025cites this paper
• Shear-driven anomalous diffusion: Memory effects and stochastic resetting

  2025cites this paper
• Response to an external field of a generalized Langevin equation with stochastic resetting of the memory kernel.

  2025cites this paper
• Manipulating Phases in Many-Body Interacting Systems with Subsystem Resetting.

  2025cites this paper
• Optimal first-passage times of active Brownian particles under stochastic resetting.

  2025cites this paper
• Impact of stochastic resetting on resource allocation: The case of reallocating geometric Brownian motion.

  2025cites this paper
• Ultraslow diffusion processes under stochastic resetting

  2025cites this paper
• Stochastic dynamical analysis, Monte-Carlo simulations, and waves dynamics of a coupled volatility and option pricing model under Brownian motion

  2025cites this paper
• GEOMETRIC BROWNIAN MOTION WITH JUMP DIFFUSION AND VALUE AT RISK ANALYSIS OF PT BANK NEGARA INDONESIA STOCKS

  2025cites this paper
• A Deep Learning-Enhanced Compartmental Model and Its Application in Modeling Omicron in China

  2024cites this paper
• Short-time expansion of one-dimensional Fokker-Planck equations with heterogeneous diffusion.

  2024cites this paper
• Multifractal-spectral features enhance classification of anomalous diffusion

  2024cites this paper
• Optimizing leapover lengths of Lévy flights with resetting.

  2024cites this paper
• Granular gases under resetting.

  2024cites this paper
• Cramér Moderate Deviations for a Supercritical Galton-Watson Process with Immigration

  2024cites this paper
• Fractional heterogeneous telegraph processes: Interplay between heterogeneity, memory, and stochastic resetting.

  2024cites this paper
• Joint probability densities of an active particle coupled to two heat reservoirs

  2024cites this paper
• Dynamical behavior of passive particles with harmonic, viscous, and correlated Gaussian forces

  2024cites this paper
• Two coupled population growth models driven by Gaussian white noises.

  2024cites this paper
• Optimal conditions for first passage of jump processes with resetting.

  2024cites this paper
• Approximate waiting times for queuing systems with variable cross-correlated arrival rates

  2024cites this paper
• Parameter estimation in the stochastic SIR model via scaled geometric Brownian motion

  2024cites this paper
• Generalized arcsine laws for a sluggish random walker with subdiffusive growth

  2024cites this paper
• Anomalous diffusion of active Brownian particles in responsive elastic gels: Nonergodicity, non-Gaussianity, and distributions of trapping times.

  2024cites this paper
• Stochastic resetting in a nonequilibrium environment.

  2024cites this paper
• Control of spatiotemporal chaos by stochastic resetting.

  2024cites this paper
• Controlling noise with self-organized resetting

  2023cites this paper
• An Epidemiological Analysis for Assessing and Evaluating COVID-19 Based on Data Analytics in Latin American Countries

  2023cites this paper
• Stochastic Differential Equations with Transformed Anticipating Conditions

  2023cites this paper
• Exploring Factors Influencing Changes in Incidence and Severity of Multisystem Inflammatory Syndrome in Children

  2023cites this paper
• Brownian particles in a periodic potential corrugated by disorder: Anomalous diffusion and ergodicity breaking

  2023cites this paper
• Ornstein–Uhlenbeck Process on Three-Dimensional Comb under Stochastic Resetting

  2023cites this paper
• A first passage under resetting approach to income dynamics

  2023cites this paper
• Anomalous diffusion, nonergodicity, non-Gaussianity, and aging of fractional Brownian motion with nonlinear clocks.

  2023cites this paper
• Modeling volatility of disaster-affected populations: A non-homogeneous geometric-skew Brownian motion approach

  2023cites this paper
• On the Telegraph Process Driven by Geometric Counting Process with Poisson-Based Resetting

  2023cites this paper
• Multifractal foundations of biomarker discovery for heart disease and stroke

  2023cites this paper
• Random Walks on Comb-like Structures under Stochastic Resetting

  2023cites this paper
• Quest for optimal quantum resetting: Protocols for a particle on a chain.

  2023cites this paper
• Dynamical Analysis of a Fractional Order Prey–Predator Model in Crowley–Martin Functional Response with Prey Harvesting

  2023cites this paper
• Customizing Random Replacement Model and Flexible Warranty Model from the Perspective of Screening Reliability

  2023cites this paper
• Multifractal descriptors ergodically characterize non-ergodic multiplicative cascade processes

  2023cites this paper
• Ergodic characterization of nonergodic anomalous diffusion processes

  2023cites this paper
• Ornstein-Uhlenbeck process and generalizations: Particle dynamics under comb constraints and stochastic resetting.

  2023cites this paper
• Striking universalities in stochastic resetting processes

  2023cites this paper
• Approximate waiting times for queuing systems with variable long-term correlated arrival rates

  2023cites this paper
• Reproducible biomarkers: Leveraging nonlinear descriptors in the face of non-ergodicity

  2023cites this paper
• Time-dependent probability density function for partial resetting dynamics

  2023cites this paper
• Exotic option pricing model of the Black–Scholes formula: a proactive investment strategy

  2023cites this paper
• Restoring ergodicity of stochastically reset anomalous-diffusion processes

  2022cites this paper
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting

  2022cites this paper
• Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic

  2022cites this paper
• Infinite ergodicity in generalized geometric Brownian motions with nonlinear drift.

  2022cites this paper
• Time-averaging and nonergodicity of reset geometric Brownian motion with drift.

  2022cites this paper
• Simulating the Spread of Infection in Networks with Quantum Computers

  2022cites this paper
• Diffusion with partial resetting.

  2022cites this paper
• The Fate of the American Dream: A First Passage Under Resetting Approach to Income Dynamics

  2022cites this paper
• Anomalous transport tuned through stochastic resetting in the rugged energy landscape of a chaotic system with roughness.

  2022cites this paper
• The predictive power of power-laws: An empirical time-arrow based investigation

  2022cites this paper
• Universality of delay-time averages for financial time series: analytical results, computer simulations, and analysis of historical stock-market prices

  2021cites this paper
• Ergodic characterization of nonergodic anomalous diffusion Ergodic characterization of nonergodic anomalous diffusion processes processes

  year unknowncites this paper