The sub-prime crisis in the U.S. reveals the limitation of diversification strategy based on mean–variance analysis. A regime switch and a turning point can be observed using a high moment representation and time-dependent transition probability. Up–down price movements are induced by...

An empirical and theoretical analysis of financial crises is conducted based on statistical mechanics in non-equilibrium physics. The transition probability provides a new tool for diagnosing a changing market. Both calm and turbulent markets can be described by the birth–death process for...

Mathematical descriptions of birth–death–movement processes are often calibrated to measurements from cell biology experiments to quantify tissue growth rates. Here we describe and analyze a discrete model of a birth–death–movement process applied to a typical two-dimensional cell...

A birth–death lattice gas model about the influence of an environment on the fitness and concentration evolution of economic entities is analytically examined. The model can be mapped onto a high-order logistic map. The control parameter is a (scalar) “business plan”. Conditions are...