## Electronic Communications in Probability

### Information loss on Gaussian Volterra process

Arturo Valdivia

#### Abstract

Gaussian Volterra processes are processes of the form $(X_{t}:=\int _{\mathbf{T} }k(t,s)\mathrm{d} W_{s})_{t\in \mathbf{T} }$ where $(W_{t})_{t\in \mathbf{T} }$ is Brownian motion, and $k$ is a deterministic Volterra kernel. On integrating the kernel $k$ an information loss may occur, in the sense that the filtration of the Volterra process needs to be enlarged in order to recover the filtration of the driving Brownian motion. In this note we describe such enlargement of filtrations in terms of the Volterra kernel. For kernels of the form $k(t,s)=k(t-s)$ we provide a simple criterion to ensure that the aforementioned filtrations coincide.

#### Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 60, 5 pp.

Dates
Accepted: 9 August 2017
First available in Project Euclid: 25 October 2017

https://projecteuclid.org/euclid.ecp/1508896983

Digital Object Identifier
doi:10.1214/17-ECP79

Mathematical Reviews number (MathSciNet)
MR3724558

Zentralblatt MATH identifier
06797813

#### Citation

Valdivia, Arturo. Information loss on Gaussian Volterra process. Electron. Commun. Probab. 22 (2017), paper no. 60, 5 pp. doi:10.1214/17-ECP79. https://projecteuclid.org/euclid.ecp/1508896983

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