arXiv subjects

Moshe Zakai

Publications and source records attributed to Moshe Zakai.

4 recordsLinked to original sources

arXiv2022

The Distribution Route from Ancestors to Descendants

We add here compared to our former arXiv version an explicit expression for the descendant ratio along the generations The equation that is added here appeared in the Hebrew version published in BDD, Bar Ilan University Press, 23, 71, 2010, titled The distribution route from ancestors to descendants in Equation 11. Otherwise, we don not change nor show here the paper but leave and direct the reader to the former arXiv version with the above addition or to the published paper in Hebrew.

q-bio.PE↗

arXiv2007

Some relations between mutual information and estimation error in Wiener space

The model considered is that of ``signal plus white noise.'' Known connections between the noncausal filtering error and mutual information are combined with new ones involving the causal estimation error, in a general abstract setup. The results are shown to be invariant under a wide class of causality patterns; they are applied to the derivation of the causal estimation error of a Gaussian nonstationary filtering problem and to a multidimensional extension of the Yovits--Jackson formula.

math.PR↗

arXiv2006

Sufficient Conditions for the Invertibility of Adapted Perturbations of Identity on the Wiener Space

Let $(W,H,μ)$ be the classical Wiener space. Assume that $U=I_W+u$ is an adapted perturbation of identity, i.e., $u:W\to H$ is adapted to the canonical filtration of $W$. We give some sufficient analytic conditions on $u$ which imply the invertibility of the map $U$. In particular it is shown that if $u\in \DD_{p,1}(H)$ is adapted and if $\exp({1/2}\|\nabla u\|_2^2-δu)\in L^q(μ)$, where $p^{-1}+q^{-1}=1$, then $I_W+u$ is almost surely invertible. As a consequence, if, there exists an integer $k\geq 1$ such that $\|\nabla^k u\|_{H^{\otimes(k+1)}}\in L^\infty(μ)$, then $I_W+u$ is again almost surely invertible.

math.PR↗

arXiv2005

On mutual information, likelihood-ratios and estimation error for the additive Gaussian channel

This paper considers the model of an arbitrary distributed signal x observed through an added independent white Gaussian noise w, y=x+w. New relations between the minimal mean square error of the non-causal estimator and the likelihood ratio between y and ωare derived. This is followed by an extended version of a recently derived relation between the mutual information I(x;y) and the minimal mean square error. These results are applied to derive infinite dimensional versions of the Fisher information and the de Bruijn identity. The derivation of the results is based on the Malliavin calculus.

math.PR↗