We define a class of not necessarily linear C0-semigroups (Pt)t≥0 on Cb(E) (more generally, on Cκ(E):=1κCb(E), for some growth bounding continuous function κ) equipped with the mixed topology τM1 for a large class of topological state spaces E. In the linear case we prove that such...

We define a class of not necessarily linear C0-semigroups (Pt)t≥0 on Cb(E) (more generally, on Cκ(E):=1κCb(E), for some growth bounding continuous function κ) equipped with the mixed topology τM1 for a large class of topological state spaces E. In the linear case we prove that such...

Stochastic filtering is defined as the estimation of a partially observed dynamical system. Approximating the solution of the filtering problem with Gaussian mixtures has been a very popular method since the 1970s. Despite nearly fifty years of development, the existing work is based on the...

We establish a large deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, the large deviation principle is derived for super-Brownian motion and Fleming–Viot process.

<Para ID="Par1">Large spatial data sets require innovative techniques for computationally efficient statistical estimation. In this comment some aspects of local predictor selection are explored, with a view towards spatially coherent field prediction and uncertainty quantification. Copyright Sociedad de...</para>