Free Jacobi Process
Free Jacobi Process
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自由雅可比过程
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
N. Demni
中科院分区：
文献类型：
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作者：
N. Demni
摘要
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.