In this paper we study ergodicity and mixing property of some measure preserving transformations on the Wiener space (W, H, µ) which are generated by some random unitary operators defined on the Cameron-Martin space H.

The construction, in [1], of a pseudodifferential calculus analogous to the Weyl calculus, an infinite dimensional setting, required introduction convenient symbol classes. symbols are functions defined on Hilbert space H, which compels us investigate, particular, their stochastic extensions Wiener linked with H.

We prove a conjecture of Nadjafi-Arani et al. on the difference between the Szeged and the Wiener index of a graph (M. J. Nadjafi-Arani, H. Khodashenas, A. R. Ashrafi: Graphs whose Szeged and Wiener numbers differ by 4 and 5, Math. Comput. Modelling 55 (2012), 1644–1648). Namely, if G is a 2-connected non-complete graph on n vertices, then Sz (G) −W (G) ≥ 2n − 6. Furthermore, the equality is ob...

We consider the class of all the Hermite processes (Z t )t2[0;1] of order q 2 N and with Hurst index H 2 ( 1 2 ; 1). The process Z (q;H) is H-self-similar, it has stationary increments and it exhibits long-range dependence identical to that of fractional Brownian motion (fBm). For q = 1, Z is fBm, which is Gaussian; for q = 2, Z is the Rosenblatt process, which lives in the second Wiener chaos;...

Let (W,H,μ) be the classical Wiener space, assume that U = IW + u is an adapted perturbation of identity satisfying the Girsanov identity. Then, U is invertible if and only if the kinetic energy of u is equal to the relative entropy of the measure induced with the action of U on the Wiener measure μ, in other words U is invertible if and only if 1 2 ∫

QSPR study on benzene derivatives have been made using recently introduced topological methodology. In this study the relationship between the Randic' (x'), Balaban (J), Szeged (Sz),Harary (H), Wiener (W), HyperWiener and Wiener Polarity (WP) to the thermal energy (Eth), heat capacity (CV) and entropy (S) of benzene derivatives is represented. Physicochemical properties are taken from the quant...

An extended stochastic gradient algorithm is developed to estimate the parameters of Hammerstein–Wiener ARMAX models. The basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo-linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates. The obtained parameter estimates of the identif...

qspr study on benzene derivatives have been made using recently introduced topological methodology. in this study the relationship between the randic' (x'), balaban (j), szeged (sz),harary (h), wiener (w), hyperwiener and wiener polarity (wp) to the thermal energy (eth), heat capacity (cv) and entropy (s) of benzene derivatives is represented.physicochemical properties are taken from the quantu...

Common motion compensated hybrid video coding standards such as H.263, MPEG-1, MPEG-2, MPEG-4 are based on a fractional-pel displacement vector (DV) resolution of 1/2-pel. Recent approaches like MPEG-4 (ACE-profile) and H.26L use higher DV resolutions of 1/4-pel and 1/8-pel. In order to estimate and compensate fractional-pel displacements, the image signal has to be interpolated. Especially for...

1 The Wiener Process The stochastic process W t is a Wiener Process if its increments are normally distributed: W t − W s ∼ N (0, t − s) (1) and are independent if non-overlapping: E{(W t 1 − W s 1)(W t 2 − W s 2)} = 0 if (s 1 , t 1) ∩ (s 2 , t 2) = ∅ (2) In particular, we have E{W t − W s } = 0 (3) E{(W t − W s) 2 } = t − s (4) Furthermore, if we fix the initial value of the process to be zero...