Opuscula Math. 38, no. 2 (2018), 261-283
https://doi.org/10.7494/OpMath.2018.38.2.261

Opuscula Mathematica

# Stochastic differential equations for random matrices processes in the nonlinear framework

Sara Stihi
Hacène Boutabia

Abstract. In this paper, we investigate the processes of eigenvalues and eigenvectors of a symmetric matrix valued process $$X_{t}$$, where $$X_{t}$$ is the solution of a general SDE driven by a $$G$$-Brownian motion matrix. Stochastic differential equations of these processes are given. This extends results obtained by P. Graczyk and J. Malecki in [Multidimensional Yamada-Watanabe theorem and its applications to particle systems, J. Math. Phys. 54 (2013), 021503].

Keywords: $$G$$-Brownian motion matrix, $$G$$-stochastic differential equations, random matrices, eigenvalues, eigenvectors.

Mathematics Subject Classification: 60B20, 60H10, 60H05.

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• Sara Stihi
• LaPS Laboratory, Badji-Mokhtar University, PO BOX 12, Annaba 23000, Algeria
• Hacène Boutabia
• LaPS Laboratory, Badji-Mokhtar University, PO BOX 12, Annaba 23000, Algeria
• LaPS Laboratory, Badji-Mokhtar University, PO BOX 12, Annaba 23000, Algeria
• Communicated by Palle E.T. Jorgensen.
• Revised: 2017-10-08.
• Accepted: 2017-10-10.
• Published online: 2017-12-29.