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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