45 research outputs found
Approximate solutions of stochastic differential delay equations with Markovian switching
Our main aim is to develop the existence theory for the solutions to stochastic differential delay equations with Markovian switching (SDDEwMSs) and to establish the convergence theory for the Euler-Maruyama approximate solutions under the local Lipschitz condition. As an application, our results are used to discuss a stochastic delay population system with Markovian switching
Boundary driven zero-range processes in random media
The stationary states of boundary driven zero-range processes in random media
with quenched disorder are examined, and the motion of a tagged particle is
analyzed. For symmetric transition rates, also known as the random barrier
model, the stationary state is found to be trivial in absence of boundary
drive. Out of equilibrium, two further cases are distinguished according to the
tail of the disorder distribution. For strong disorder, the fugacity profiles
are found to be governed by the paths of normalized -stable
subordinators. The expectations of integrated functions of the tagged particle
position are calculated for three types of routes.Comment: 23 page
Convergence in distribution of minimum-distance estimators
It is shown that (under some regularity conditions) minimum distance estimators for a (possibly multidimensional) real parameter of a family of univariate continuous distribution functions have an asymptotic distribution. If the distance is derived from the mean-square norm it is proved that the asymptotic distribution is normal. Weak convergence of empirical distribution to the Brownian bridge is the essential tool for the proof