Phenomenology of stochastic exponential growth

Abstract

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, Geometric Brownian Motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

Physical Review E, 2017

References in corpus (3)

• Scaling laws governing stochastic growth and division of single bacterial cells
• Universality in stochastic exponential growth
• Long-run growth rate in a random multiplicative model

Cited by in corpus (9)

• Bridging the time scales of single-cell and population dynamics
• Cell size regulation induces sustained oscillations in the population growth rate
• Master equation approach to the stochastic accumulation dynamics of bacterial cell cycle
• Asymptotic decoupling of population growth rate and cell size distribution
• Cell cycle length and long-time behaviour of an age-size model
• Competition between transient oscillations and early stochasticity in exponentially growing populations
• The Two-Particle Irreducible Effective Action for Classical Stochastic Processes
• Exactly Solvable Population Model with Square-Root Growth Noise and Cell-Size Regulation
• Emergent Simplicities in the Living Histories of Individual Cells