This paper considers the dynamic evolution of algorithmic (recursive) learning rules in a normal form game. It is shown that the system | the population frequencies | is globally stable for any arbitrary N -player normal form game, if the evolutionary process is algorithmic and the `birth process' guarantees that an appropriate set of `smart' rules is present in the population. The result is in...

Pure stochastic birth process models are used to establish the connection between the traditional food microbiology concept of bacterial lag period, before the exponential growth, and the distribution of the lag times of individual cells. In a parallel way, similar study is carried out on the connection between the "shoulder" period, before the exponential decay, and the distribution of the sur...

Spectral measures and transition probabilities of birth and death processes with A0 #o 0 are obtained as limite when Ao 0+ of the corresponding quantities. In pa,rticula th(, case of finite population is discussed in full detail. Pure birth and death processes are used to derive an inequality for Dirichlet polynomials.

This paper presents a new Bayesian method that can incorporate knowledge gained from past experience to improve early forecasting of new products and services. The method is based on maximum likelihood estimation of a pure birth process with a Bass-type adoption rate that can capture price and promotion effects. Direct maximum likelihood estimation of the model parameters is numerically infeasi...

In this work we study the limit distribution of an appropriately normalized cophenetic index of the pure–birth tree conditioned on n contemporary tips. We show that this normalized phylogenetic balance index is a submartingale that converges almost surely and in L2. We link our work with studies on trees without branch lengths and show that in this case the limit distribution is a contraction–t...