Abstract

Time-changed stochastic processes revealed a powerful tool to model the behaviour of phenomena subject to memory effects. One of the benefit of the stochastic time change is just to provide models evolving in correspondence to the occurrence of time events. We show how it will be possible to adopt a time-changed stochastic process for modelling the interaction between the myosin head and the actin filament, the physio-chemical mechanism triggering the muscle contraction and now not completely understood. We describe such features from a theoretical point of view and with simulations of sample paths. Mean functions and covariances are provided considering constant and time-dependent tilting forces by which effects of external loads are included. The investigation of the dwell time of such phenomenon is carried out by means of density estimations of the first exit time (FET) of the processes from a strip: this mimics the times of the steps of the myosin head during the sliding movement outside a potential well due to the interaction with the actin. Some numerical and simulation results are given and discussed. These results are based on a joint work with Nikolai Leonenko. Furthermore, we also show how a time-changed Poisson process can be used in the risk theory. In particular, we put in evidence some results obtained in the study of a time-changed risk model.

These results are based on a joint work with Nikolai Leonenko, Andrey Pepelyshev, Alois Pichler and Xiangyun Meng.

Seminars in Probability and Finance