This paper focuses on the problem of Kalman filtering for Itô stochastic continuous-time systems with multiple delayed measurements, for which very little work exist to date. For an Itô-stochastic system, its stochastic differential and integral have a significant place and are different from other stochastic systems owing to the Wiener or the Brownian process. In this paper, an Itô stochastic ...

We investigate stochastic Volterra equations and their limiting laws. The we consider are driven by a Hilbert space valued \Levy noise integration kernels may have non-linear dependence on the current state of process. Our method is based an embedding into functions which allows to represent solution equation as boundary value partial differential equation. first gather abstract results give mo...

Stochastic integration with respect to a Wiener process in Banach spaces have been considered by several authors (Brzeźniak [5], Dettweiler [13], Neidhart [22] and Van Neerven, Veraar and Weiss [30]). Similarly, stochastic integration with respect to Lévy processes in Banach spaces is of increasing interest. So, these articles [2, 3, 7, 15, 24, 25] are devoted to this topic. Nevertheless, in th...

In [3] we introduced a “monotone-type” (that is, Choquet-type) integral for realvalued functions, with respect to finitely additive positive set functions, with values in a Dedekind complete Riesz space. A “Lebesgue-type” integral for such kind of functions was investigated in [7]. In [4] we gave some comparison results for these types of integrals. In [10], a Choquet-type integral for real-val...