Ito formula for free stochastic integrals

Regularity of distributions of Wigner integrals

Wigner integrals and the corresponding Wigner chaos were introduced by P. Biane and R. Speicher in 1998 as a non-commutative counterpart of classical Wiener-Itô integrals and the corresponding Wiener-Itô chaos, respectively, in free probability. In the classical case, a famous result of I. Shigekawa states that non-trivial elements in the finite Wiener-Itô chaos have an absolutely continuous distribution. We provide here a first contribution to such regularity questions for Wigner integrals by showing that the distribution of non-trivial elements in the finite Wigner chaos cannot have atoms. T…

自由 Itô 过程的非交换 $C^2$ 函数的 Itô 公式

Itô's formula for noncommutative $C^2$ functions of free Itô processes

本文证明自伴自由 Itô 过程的非交换 C² 函数的 Itô 公式，将函数类从 Biane-Speicher 空间扩展到 NC²(ℝ)，并给出带迹公式及矩阵情形的动机。