On the equivalence of the centered Gaussian measure in L 2 with the correlation operator (−d 2/dx 2)−1 and the conditional Wiener measure

2009 ◽  
Vol 58 (3) ◽  
pp. 427-440 ◽  
Author(s):  
Peter Zhidkov
Keyword(s):  
Gaussian Measure ◽  
Wiener Measure ◽  
Correlation Operator

scholarly journals Gaussian Measure on a Banach Space and Abstract Winer Measure

1969 ◽  
Vol 36 ◽  
pp. 65-81 ◽  
Author(s):  
Hiroshi Sato
Keyword(s):  
Banach Space ◽  
Gaussian Measure ◽  
Reflexive Banach Space ◽  
Wiener Measure

In this paper, we shall show that any Gaussian measure on a separable or reflexive Banach space is an abstract Wiener measure in the sense of L. Gross [1] and, for the proof of that, establish the Radon extensibility of a Gaussian measure on such a Banach space. In addition, we shall give some remarks on the support of an abstract Wiener measure.

scholarly journals Intermediate spaces, Gaussian probabilities and exponential tightness

2021 ◽  
Author(s):  
Paolo Baldi
Keyword(s):  
Banach Space ◽  
Gaussian Measure ◽  
Wiener Measure ◽  
Intermediate Space ◽  
Exponential Tightness

AbstractWe prove the existence of an intermediate Banach space between the space where the Gaussian measure lives and its RKHS, thus extending what happens with Wiener measure, where the intermediate space can be chosen as a space of Hölder paths. From this result, it is very simple to deduce a result of exponential tightness for Gaussian probabilities.

scholarly journals On Abstract Wiener Measure

1972 ◽  
Vol 46 ◽  
pp. 155-160 ◽  
Author(s):  
Balram S. Rajput
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Gaussian Measure ◽  
Separable Hilbert Space ◽  
Reflexive Banach Space ◽  
Wiener Measure ◽  
Real Separable Hilbert Space ◽  
Cylinder Measure

In a recent paper, Sato [6] has shown that for every Gaussian measure n on a real separable or reflexive Banach space (X, ‖ • ‖) there exists a separable closed sub-space X〵 of X such that and is the σ-extension of the canonical Gaussian cylinder measure of a real separable Hilbert space such that the norm is contiunous on and is dense in The main purpose of this note is to prove that ‖ • ‖ x〵 is measurable (and not merely continuous) on .

Polar Decomposition of Wiener Measure and Schwarzian Integrals

2020 ◽  
Vol 41 (4) ◽  
pp. 709-713
Author(s):  
E. T. Shavgulidze ◽  
N. E. Shavgulidze
Keyword(s):  
Polar Decomposition ◽  
Wiener Measure

scholarly journals On the lack of dimension-free estimates in Lp for maximal functions associated to radial measures

2010 ◽  
Vol 140 (3) ◽  
pp. 541-552 ◽  
Author(s):  
Alberto Criado
Keyword(s):  
Gaussian Measure ◽  
Maximal Operator ◽  
Recent Article ◽  
Maximal Functions

In a recent article Aldaz proved that the weak L1 bounds for the centred maximal operator associated to finite radial measures cannot be taken independently with respect to the dimension. We show that the same result holds for the Lp bounds of such measures with decreasing densities, at least for small p near to one. We also give some concrete examples, including the Gaussian measure, where better estimates with respect to the general case are obtained.

Sign in / Sign up

Export Citation Format

Share Document