Convergence for global curve diffusion flows

Uniform convergence of curve estimators for ergodic diffusion processes

Diffusion Approximations for Online Principal Component Estimation and Global Convergence

In this paper, we propose to adopt the diffusion approximation tools to study the dynamics of Oja’s iteration which is an online stochastic gradient descent method for the principal component analysis. Oja’s iteration maintains a running estimate of the true principal component from streaming data and enjoys less temporal and spatial complexities. We show that the Oja’s iteration for the top ei...

Rates of convergence and asymptotic normality of curve estimators for ergodic diffusion processes

Bäcklund Transformations for Integrable Geometric Curve Flows

We study the Bäcklund transformations of integrable geometric curve flows in certain geometries. These curve flows include the KdV and Camassa-Holm flows in the two-dimensional centro-equiaffine geometry, the mKdV and modified Camassa-Holm flows in the two-dimensional Euclidean geometry, the Schrödinger and extended Harry-Dym flows in the three-dimensional Euclidean geometry and the Sawada-Kote...

Convergence Curve for Non-Blind Adaptive Equalizers

In this paper a closed-form approximated expression is proposed for the Intersymbol Interference (ISI) as a function of time valid during the entire stages of the non-blind adaptive deconvolution process and is suitable for the noisy, real and two independent quadrature carrier input case. The obtained expression is applicable for type of channels where the resulting ISI as a function of time c...