A stochastic hybrid system, also known as a switching diffusion, is continuous-time Markov process with state space consisting of discrete and continuous parts. We consider parametric estimation the Q matrix for transitions drift coefficient diffusion part. First, we derive likelihood function under complete observation sample path in continuous-time. Then, extending finite-dimensional filter h...

A deterministic function of a Markov process is called an aggregated Markov process. We give necessary and suucient conditions for the equivalence of continuous-time aggregated Markov processes. For both discrete-and continuous-time, we show that any aggregated Markov process which satisses mild regularity conditions can be directly converted to a canonical representation which is unique for ea...

We consider quantization from the perspective of minimizing filtering error when quantized instead of continuous measurements are used as inputs to a nonlinear filter, specializing to discrete-time two-state hidden Markov models (HMMs) with continuous-range output. An explicit expression for the filtering error when continuous measurements are used is presented. We also propose a quantization s...