Abstract
Using a matrix approach, we define free Wishart processes of parameter λ > 0 and prove a free additivity property and invertibility for λ > 1. For λ ≥ 1, we show that a free Wishart process is a solution of a SDE of square Bessel process type, driven by a free complex Brownian motion. In the case λ > 1, we establish existence and uniqueness of a strong solution of such a SDE.
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Capitaine, M., Donati-Martin, C. Free Wishart Processes. J Theor Probab 18, 413–438 (2005). https://doi.org/10.1007/s10959-005-3511-z
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DOI: https://doi.org/10.1007/s10959-005-3511-z