## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 29, Number 4 (2015), 733-746.

### Occupation densities for certain processes related to subfractional Brownian motion

Ibrahima Mendy and Ibrahim Dakaou

#### Abstract

In this paper, we establish the existence of a square integrable occupation density for two classes of stochastic processes. First, we consider a Gaussian process with an absolutely continuous random drift, and second we handle the case of a (Skorohod) integral with respect to subfractional Brownian motion with Hurst parameter $H>\frac{1}{2}$. The proof of these results uses a general criterion for the existence of a square integrable local time, which is based on the techniques of Malliavin calculus.

#### Article information

**Source**

Braz. J. Probab. Stat., Volume 29, Number 4 (2015), 733-746.

**Dates**

Received: April 2013

Accepted: April 2014

First available in Project Euclid: 17 September 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1442513443

**Digital Object Identifier**

doi:10.1214/14-BJPS243

**Mathematical Reviews number (MathSciNet)**

MR3397390

**Zentralblatt MATH identifier**

1334.60056

**Keywords**

Subfractional Brownian motion Malliavin calculus Skorohod integral local time

#### Citation

Mendy, Ibrahima; Dakaou, Ibrahim. Occupation densities for certain processes related to subfractional Brownian motion. Braz. J. Probab. Stat. 29 (2015), no. 4, 733--746. doi:10.1214/14-BJPS243. https://projecteuclid.org/euclid.bjps/1442513443