The restoration achieved on the basis of a Wiener scheme is an optimum since the restoration filter is the outcome of a minimisation process. Moreover, the Wiener restoration approach requires the estimation of some parameters related to the original image and the noise, as well as knowledge about the PSF function. However, in a real restoration problem, we may not possess accurate values of th...

We examine the question of determining the "best" linear filter, in an expected squared error sense, for a signal generated by stochastic linear differential equation on a Hilbert space. Our results, which extend the development in Kalman and Bucy (1960), rely heavily on the integration theory for Banach-space-valued functions of Dunford and Schwartz (1958). In order to derive the Kalman-Bucy f...

Abstract. In this paper Reverse Wiener index, Reverse Detour Wiener index, Reverse Circular Wiener index Reverse Harary index, Reverse Detour Harary index, Reverse Circular Harary index, Reverse Reciprocal Wiener index, Reverse Detour Reciprocal Wiener index, Reverse Circular Reciprocal Wiener index, Reverse Hyper Wiener index, Reverse, Detour Hyper Wiener index, Reverse Circular Hyper Wiener i...

Let λ(T,aT ,α) = { 2aT [ log T aT + α log log T + (1− α) log log aT ]}− 2 where 0 ≤ α ≤ 1 and {W (t), t ≥ 0} be a standard Wiener process. This paper studies the almost sure limiting behaviour of sup 0≤t≤T−aT λ(T,aT ,α)|W (t+aT )−W (t)| as T −→∞ under varying conditions on aT and T aT .