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Article Dans Une Revue Journal of Mathematical Physics Année : 2013

Multidimensional Yamada-Watanabe theorem and its applications to particle systems

Résumé

We prove a multidimensional version of the Yamada-Watanabe theorem, i.e., a theorem giving conditions on coefficients of a stochastic differential equation for existence and pathwise uniqueness of strong solutions. It implies an existence and uniqueness theorem for the eigenvalue and eigenvector processes of matrix-valued stochastic processes, called a “spectral” matrix Yamada-Watanabe theorem. The multidimensional Yamada-Watanabe theorem is also applied to particle systems of squared Bessel processes, corresponding to matrix analogues of squared Bessel processes, Wishart and Jacobi matrix processes. The β-versions of these particle systems are also considered.

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Dates et versions

hal-03038367 , version 1 (03-12-2020)

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Piotr Graczyk, Jacek Małecki. Multidimensional Yamada-Watanabe theorem and its applications to particle systems. Journal of Mathematical Physics, 2013, 54 (2), pp.021503. ⟨10.1063/1.4790507⟩. ⟨hal-03038367⟩
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