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Full-Text Articles in Other Mathematics
On Free Stochastic Processes And Their Derivatives, Daniel Alpay, Palle Jorgensen, Guy Salomon
On Free Stochastic Processes And Their Derivatives, Daniel Alpay, Palle Jorgensen, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study a family of free stochastic processes whose covariance kernels K may be derived as a transform of a tempered measure σ. These processes arise, for example, in consideration non-commutative analysis involving free probability. Hence our use of semi-circle distributions, as opposed to Gaussians. In this setting we find an orthonormal bases in the corresponding noncommutative L2 of sample-space. We define a stochastic integral for our family of free processes.
Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory, Daniel Alpay, Guy Salomon
Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.