We are concerned with estimating the mode of a density spatial process by kernel method under some dependency conditions. A simple estimate based only on data is considered. The approach consists maximising data. An optimal rate uniform consistency will be established. Strong investigated when spatially dependent general mixing

The paper proposes a simple approximate method for solving differential equations boundary value problems. A is proposed averaging over moving volume, which allows obtaining analytical solutions of equations. control volume the only one in considered area problem. In this case, to be moved under consideration. Based on problems being moved, an algebraic equation obtained. When variables (in cas...

Epidemic processes on random graphs or networks are marked by localization of activity that can trap the dynamics into a metastable state, confined to subextensive part network, before visiting an absorbing configuration. Quasistationary (QS) method is technique deal with states for finite sizes and has played central role in investigation epidemic heterogeneous where hallmark. The standard QS ...

We investigate simple models for strictly non-ergodic stochastic processes $$x_t$$ (t being the discrete time step) focusing on expectation value v and standard deviation $$\delta v$$ of empirical variance $$v[\mathbf {x}]$$ finite series $$\mathbf {x}$$ . is averaged over a fluctuating field $$\sigma _{\mathbf{r}}$$ ( $$\mathbf{r}$$ microcell position) characterized by quenched spatially corre...