In this work, we consider linear and nonlinear fractional stochastic delay systems driven by the Rosenblatt process. With aid of delayed Mittag-Leffler matrix functions representation solutions these systems, derive controllability results as an application. By introducing a Gramian matrix, provide sufficient necessary criteria for systems. Furthermore, employing Krasnoselskii’s fixed point the...

In this work, we consider dynamical systems of linear and nonlinear stochastic delay-differential equations driven by the Rosenblatt process. With aid delayed matrix functions these systems, derive controllability results as an application. By using a delay Gramian matrix, provide sufficient necessary criteria for systems. addition, employing Krasnoselskii’s fixed point theorem, present some Ou...

In this tutorial paper we give an overview of deconvolution problems in nonparametric statistics. First, we consider the problem of density estimation given a contaminated sample. We illustrate that the classical Rosenblatt-Parzen kernel density estimator is unable to capture the full shape of the density while the presented method experiences almost no problems. Second, we use the previous est...

TPT-RAID is a multi-box RAID wherein each ECC group comprises at most one block from any given storage box, and can thus tolerate a box failure. It extends the idea of an out-of-band SAN controller into the RAID: data is sent directly between hosts and targets and among targets, and the RAID controller supervises ECC calculation by the targets. By preventing a communication bottleneck in the co...

In this paper, we prove a Donsker type approximation theorem for the Rosenblatt process, which is a selfsimilar stochastic process exhibiting long range dependence. By using numerical results and simulated data, we show that this approximation performs very well. We use this result to construct a binary market model driven by this process and we show that the model admits arbitrage opportunitie...