1 citations · 2 across the 10 of their papers we have counts for
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Gaussian processes in Non-commutative probability
Palle E. T. Jorgensen, James Tian
Motivated by questions in quantum theory, we study Hilbert space valued Gaussian processes, and operator-valued kernels, i.e., kernels taking values in B(H) (= all bounded linear o…
From Classical to Quantum: Polymorphisms in Non-Commutative Probability
Palle E. T. Jorgensen, James Tian
We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classic…
Operator-Valued Kernels, Machine Learning, and Dynamical Systems
Palle E. T. Jorgensen, James Tian
In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. W…
Hilbert space-valued Gaussian processes, and quantum states
Palle E. T. Jorgensen, James Tian
We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as…
Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure
Palle E. T. Jorgensen, James Tian
Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stoch…