## The Annals of Probability

- Ann. Probab.
- Volume 11, Number 1 (1983), 46-57.

### Gaussian Measures in $B_p$

Naresh C. Jain and Ditlev Monrad

#### Abstract

For $p \geq 1$, conditions for a separable Gaussian process to have sample paths of finite $p$-variation are given in terms of the mean function and the covariance function. A process with paths of finite $p$-variation may or may not induce a tight measure on the nonseparable Banach space $B_p$. Consequences of tightness and conditions for tightness are given.

#### Article information

**Source**

Ann. Probab., Volume 11, Number 1 (1983), 46-57.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993659

**Digital Object Identifier**

doi:10.1214/aop/1176993659

**Mathematical Reviews number (MathSciNet)**

MR682800

**Zentralblatt MATH identifier**

0504.60045

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60G15: Gaussian processes

Secondary: 60G17: Sample path properties 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)

**Keywords**

Stochastic processes Gaussian sample paths $p$-variation nonseparable Banach spaces induced measure tightness

#### Citation

Jain, Naresh C.; Monrad, Ditlev. Gaussian Measures in $B_p$. Ann. Probab. 11 (1983), no. 1, 46--57. doi:10.1214/aop/1176993659. https://projecteuclid.org/euclid.aop/1176993659