Free Jacobi Process

N. Demni ()
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N. Demni: Université de Paris VI

Journal of Theoretical Probability, 2008, vol. 21, issue 1, 118-143

Abstract: Abstract In this paper, we define and study two parameters dependent free processes (λ,θ) called free Jacobi, obtained as the limit of its matrix counterpart when the size of the matrix goes to infinity. The main result we derive is a free SDE analogous to that satisfied in the matrix setting, derived under injectivity assumptions. Once we did, we examine a particular case for which the spectral measure is explicit and does not depend on time (stationary). This allows us to determine easily the parameters range ensuring our injectivity requirements so that our result applies. Then, we show that under an additional condition of invertibility at time t=0, this range extends to the general setting. To proceed, we set a recurrence formula for the moments of the process via free stochastic calculus.

Keywords: Unitary Brownian matrix; Free Jacobi process; Free additive Brownian motion; Free multiplicative Brownian motion; Polar decomposition (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-007-0110-1

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