Journal of Probability http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Wiener-Itô Chaos Expansion of Hilbert Space Valued Random Variables Mon, 07 Apr 2014 16:23:36 +0000 http://www.hindawi.com/journals/jprob/2014/786854/ The notion of -fold iterated Itô integral with respect to a cylindrical Hilbert space valued Wiener process is introduced and the Wiener-Itô chaos expansion is obtained for a square Bochner integrable Hilbert space valued random variable. The expansion can serve a basis for developing the Hilbert space valued analog of Malliavin calculus of variations which can then be applied to the study of stochastic differential equations in Hilbert spaces and their solutions. M. A. Alshanskiy Copyright © 2014 M. A. Alshanskiy. All rights reserved. Marshall-Olkin Discrete Uniform Distribution Mon, 07 Apr 2014 11:17:36 +0000 http://www.hindawi.com/journals/jprob/2014/979312/ We introduce and characterize a new family of distributions, Marshall-Olkin discrete uniform distribution. The natures of hazard rate, entropy, and distribution of minimum of sequence of i.i.d. random variables are derived. First order autoregressive (AR (1)) model with this distribution for marginals is considered. The maximum likelihood estimates for the parameters are found out. Also, the goodness of the distribution is tested with real data. E. Sandhya and C. B. Prasanth Copyright © 2014 E. Sandhya and C. B. Prasanth. All rights reserved.