This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study the interrelation of reactive processes and Markov chains in this setting, and introduce the algebr...

Suppose one can observe a Gaussian nonhomogeneous process with a continuous time parameter. At an unknown time the observed process may leave its standard state, the drift of the process changes and becomes equal to a nonrandom function. Subject to a restriction on the rate of false alarms, one wants to detect the change \as soon as possible". We investigate Page's and Shiryaev's sequential det...

We study a family of Markov processes on P , the space of partitions of the natural numbers with at most k blocks. The process can be constructed from a Poisson point process on R+ ×∏ki=1 P (k) with intensity dt ⊗ (k) ν , where ν is the distribution of the paintbox based on the probability measure ν on Pm, the set of ranked-mass partitions of 1, and (k) ν is the product measure on ∏k i=1 P . We...

In this article we propose a methodology for building a lognormal diffusion process with polynomial exogenous factors in order to fit data that present an exponential trend and show deviations with respect to an exponential curve in the observed time interval. We show that such a process approaches a nonhomogeneous lognormal diffusion and proves that it is specially useful in the case when exte...