Metrics on the set of semimartingale filtrations

Let X be a stochastic process with cadlag paths. We consider the set of all filtrations under which X is a semimartingale, and we define a distance between such filtrations with the help of the bounded variation parts in the corresponding decompositions of X. We show that this distance is a complete metric on the set of semimartingale filtrations if the given process X is continuous.     

Stability of stochastic SIRS epidemic models with saturated incidence rates and delay

In this article, we consider stochastic susceptible-infected-removed-susceptible (SIRS) epidemic models with saturated incidence rates and delay. We investigate the stochastic stability in probability of the disease-free and endemic equilibria for the stochastic dynamic model with variability in the natural death rate, and the stochastic stability in probability of the endemic equilibrium for the dynamic model when the variability in the environment is proportional to a deviation between the state of the system and the endemic equilibrium. The numerical experiments are provided to support our theoretical results.     

Reverse order law for generalized inverses of multiple operator product

In this paper, we consider the reverse order law for generalized inverses of operators on Hilbert spaces. We derive necessary and sufficient conditions for various inclusions concerning the reverse order law for generalized inverses of multiple operator product. We extend the finite dimensional results from (Wei M. Reverse order laws for generalized inverses of multiple matrix products. Linear Algebra Appl. 1999;293:13.) to infinite dimensional settings.