4 papers
Well-posedness of Filtering Equations in Weighted Sobolev Spaces with Unbounded System Coefficients
Zeju Sun, Songlin Zhou, Stephen S. -T. Yau
Nonlinear filtering problem is one of the core subjects in modern control theory. In this paper, we will study the well-posedness of the three fundamental evolution equations arisi…
A Lie-algebraic approach to non-Markovian quantum dynamics
Haijin Ding, Stephen S. -T. Yau, Zhiwen Zhang
In this paper, we study the non-Markovian quantum dynamics in quantum computations from the perspective of a Lie algebraic approach based on numerical analysis. By vectorizing the…
Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds
Jiayi Kang, Andrew Salmon, Stephen Shing-Toung Yau
Estimation algebras have been extensively studied in Euclidean space, where finite-dimensional estimation algebras form the foundation of the Kalman and Benes filters, and have con…
On the Convergence Analysis of Yau-Yau Nonlinear Filtering Algorithm: from a Probabilistic Perspective
Zeju Sun, Xiuqiong Chen, Stephen S. -T. Yau
At the beginning of this century, a real time solution of the nonlinear filtering problem without memory was proposed in [1, 2] by the third author and his collaborator, and it is…