consider the random walk among n places with n(n - 1)/2 transports. we attach an exponential random variable xij to each transport between places pi and pj and take these random variables mutually independent. if transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

We consider a fractional version of the classical non-linear birth process of which the YuleFurry model is a particular case. Fractionality is obtained by replacing the first-order time derivative in the difference-differential equations which govern the probability law of the process, with the Dzherbashyan-Caputo fractional derivative. We derive the probability distribution of the number Nν (t...

The homogeneous reconstructed evolutionary process is a birth-death process without observed extinct lineages. Each species evolves independently with the same diversification rate-speciation rate, λ(t), and extinction rate, μ(t)-that may change over time. The process is commonly applied to model species diversification where the data are reconstructed phylogenies, e.g. trees estimated from pre...

Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...