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- Hatem Hajri
- 2011

We define an equation on a simple graph which is an extension of Tanaka’s equation and the skew Brownian motion equation. We then apply the theory of transition kernels developed by Le Jan and Raimond and show that all the solutions can be classified by probability measures.

- Hatem Hajri, Ioana Ilea, Salem Said, Lionel Bombrun, Yannick Berthoumieu
- Entropy
- 2016

The Riemannian geometry of the space Pm, of m × m symmetric positive definite matrices, has provided effective tools to the fields of medical imaging, computer vision and radar signal processing. Still, an open challenge remains, which consists of extending these tools to correctly handle the presence of outliers (or abnormal data), arising from excessive… (More)

This paper consists in the study of a stochastic differential equation on a metric graph, called an interface SDE (ISDE). To each edge of the graph is associated an independent white noise, which drives (ISDE) on this edge. This produces an interface at each vertex of the graph. We first do our study on star graphs with N ≥ 2 rays. The case N = 2… (More)

- Hatem Hajri
- 2011

In a previous work, we have defined a Tanaka’s SDE related to Walsh Brownian motion which depends on kernels. It was shown that there are only one Wiener solution and only one flow of mappings solving this equation. In the terminology of Le Jan and Raimond, these are respectively the stronger and the weaker among all solutions. In this paper, we obtain… (More)

- Hatem Hajri, Wajdi Touhami
- 2014

1. Itô’s formula for Walsh’s Brownian motion Let E = R2; we will use polar co-ordinates (r, α) to denote points in E. We denote by C(E) the space of all continuous functions on E. For f ∈ C(E), we define fα(r) = f (r, α), r > 0, α ∈ [0, 2π [. Throughout this paper we fix μ a probability measure on [0, 2π [, also we define f (r) = 2π 0 f (r, α) μ(dα), r >… (More)

- Hatem Hajri
- 2015

We review the construction of flows associated to Tanaka’s SDE from [8]. Using the skew Brownian motion, we give an easy proof of the classification of these flows by means of probability measures on [0, 1]. Our arguments also simplify some proofs in the subsequent papers [1, 3, 9, 2].

- Ioana Ilea, Hatem Hajri, Salem Said, Lionel Bombrun, Christian Germain, Yannick Berthoumieu
- IEEE Signal Processing Letters
- 2016

This letter introduces a new robust estimation method for the central value of a set of N covariance matrices. This estimator, called Huber's centroid, is described starting from the expression of two well-known methods that are the center of mass and the median. In addition, a computation algorithm based on the gradient descent is proposed. Moreover,… (More)

We study a simple stochastic differential equation (SDE) driven by one Brownian motion on a general oriented metric graph whose solutions are stochastic flows of kernels. Under some conditions, we describe the laws of all solutions. This work is a natural continuation of [17, 8, 10] where some particular metric graphs were considered.

- HATEM HAJRI, E. Csáki, H. HAJRI
- 2013

Csáki and Vincze have defined in 1961 a discrete transformation T which applies to simple random walks and is measure preserving. In this paper, we are interested in ergodic and asymptotic properties of T . We prove that T is exact: ∩ k=1 σ(T (S)) is trivial for each simple random walk S and give a precise description of the lost information at each step k.… (More)

- Hatem Hajri, Salem Said, Lionel Bombrun, Yannick Berthoumieu
- 2017 IEEE International Conference on Acoustics…
- 2017

Many signal and image processing applications, including SAR polarimetry and texture analysis, require the classification of complex covariance matrices. The present paper introduces a geometric learning approach on the space of complex covariance matrices based on a new distribution called Riemannian Gaussian distribution. The proposed distribution has two… (More)

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