Stochastic processes for bounded noise (Q1411648)

The authors establish results on probabilistic modeling for bounded noise relying on the total order of the real line. They study the following scalar differential inclusion: \(\dot x\in f(x)+ g(x)[-1,1]\), \(x(0)= x_0\). This inclusion is considered as a model of the dynamical system \(\dot x=f(x)\) perturbed by the bounded noise \(g(x)u\), \(u\in [-1,1]\). They want to construct stochastic processes such that supports of distributions of these processes on their path spaces coincide with the set of solutions of the inclusion mentioned above, and features of these processes can be analyzed via their finite-dimensional distributions. They investigate features of Markov processes and show that these processes are not suitable models for the aforementioned requirements. They also construct non-Markov processes through their finite-dimensional distributions, which satisfy these requirements.