Stochastic dynamics simulation with generalized interval probability

Abstract

Two types of uncertainties are generally recognized in modelling and simulation, including variability caused by inherent randomness and incertitude due to the lack of perfect knowledge. In this paper, a generalized interval-probability theory is used to model both uncertainty components simultaneously, where epistemic uncertainty is quantified by generalized interval in addition to probability measure. Conditioning, independence, and Markovian probabilities are uniquely defined in generalized interval probability such that its probabilistic calculus resembles that in the classical probability theory. A path-integral approach can be taken to solve the interval Fokker–Planck equation for diffusion processes. A Krylov subspace projection method is proposed to solve the interval master equation for jump processes. Thus, the time evolution of both uncertainty components can be simulated simultaneously, which provides the lower and upper bound information of evolving probability distributions as an alternative to the traditional sensitivity analysis.

Keywords:

• aleatory uncertainty
• epistemic uncertainty
• imprecise probability
• reliable simulation
• multi-scale simulation

2010 AMS Subject Classifications:

• 60A86
• 60J60
• 60J75
• 65G40