A new class of random partial differential equations of parabolic type is considered where the stochastic term consists in an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a prob...

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unst...

Few fast statistical signal processing algorithms exist for large problems involving non-stationary processes and irregular measurements. A recently introduced class of multiscale autoregressive models indexed by trees admits signal processing algorithms which can efficiently deal with problems of this type. In this paper we provide a novel and efficient algorithm for translating any secondorde...