Random Time Change Equations and PDMPs with Applications to Numerical Analysis
Sprache des Vortragstitels:
1st Austrian Stochastics Days
Sprache des Tagungstitel:
Stochastic Hybrid System are characterised as evolving in time both continuously and in a jumping fashion. A particular important subclass are Piecewise Deterministic Markov Processes for which the continuous evolution is given by deterministic differential equations and the random jump intensities are state dependent. This class of stochastic processes has important applications in chemical reaction kinetics, mathematical neuroscience and control engineering. In my talk I will first show that a subclass of these processes often encountered in (biological) applications are equivalent to certain Random Time Change Equation. This allows to represent PDMPs as closed form stochastic evolution equations. In this representation hybrid system are much more accessible to analysis than in their classical representation. Secondly, I will present numerical methods for solving Random Time Change equations and present general strong and weak convergence result for semi-implicit Maruyama-type methods.