## Approximating Continuous Markov Processes (2000)

Citations: | 9 - 3 self |

### BibTeX

@MISC{Desharnais00approximatingcontinuous,

author = {Josée Desharnais and Radha Jagadeesan and Vineet Gupta and Prakash Panangaden},

title = {Approximating Continuous Markov Processes},

year = {2000}

}

### OpenURL

### Abstract

Markov processes with continuous state spaces arise in the analysis of stochastic physical systems or stochastic hybrid systems. The standard logical and algorithmic tools for reasoning about discrete (finite-state) systems are, of course, inadequate for reasoning about such systems. In this work we develop three related ideas for making such reasoning principles applicable to continuous systems. ffl We show how to approximate continuous systems by a countable family of finite-state probabilistic systems, we can reconstruct the full system from these finite approximants, ffl we define a metric between processes and show that the approximants converge in this metric to the full process, ffl we show that reasoning about properties definable in a rich logic can be carried out in terms of the approximants. The systems that we consider are Markov processes where the state space is continuous but the time steps are discrete. We allow such processes to interact with the environment by syn...