Hybrid Petri Nets with Diffusion That Have Into-Mappings with Generalised Stochastic Hybrid Processes

Abstract

Generalised Stochastic Hybrid Processes (GSHPs) are known as the largest class of Markov processes virtually describing all continuous-time processes including diffusion. In general, the state space of a GSHP is of hybrid type, i.e., a Kronecker product of a discrete set and a continuous-valued space. Since Stochastic Petri Nets have proven to be extremely useful in developing continuous-time Markov Chain models for complex practical discrete-valued processes, there is a clear need for a type of hybrid Petri Nets that can play a similar role for developing GSHP models for complex practical problems. To fulfil this need, the report defines a Stochastically and Dynamically Coloured Petri Net (SDCPN), and proves that there exist into-mappings between GSHPs and SDCPNs.