Bayesian prediction for a jump diffusion process - With application to crack growth in fatigue experiments

In many fields of technological developments, understanding and controlling material fatigue is an important point of interest. This article is concerned with statistical modeling of the damage process of prestressed concrete under low cyclic load. A crack width process is observed which exhibits jumps with increasing frequency. Firstly, these jumps are modeled using a Poisson process where two intensity functions are presented and compared. Secondly, based on the modeled jump process, a stochastic process for the crack width is considered through a stochastic differential equation (SDE). It turns out that this SDE has an explicit solution. For both modeling steps, a Bayesian estimation and prediction procedure is presented.