Necessary conditions for stable convergence of semimartingales

Necessary and Sufficient Conditions for Linear Convergence of `1-Regularization

Motivated from the theoretical and practical results in compressed sensing, efforts have been undertaken by the inverse problems community to derive analogous results, for instance linear convergence rates, for Tikhonov regularization with `1-penalty term for the solution of ill-posed equations. Conceptually, the main difference between these two fields is that regularization in general is an u...

Some Necessary Conditions for Convergence of the Gbdf Methods

The Generalized Backward Differentiation methods for solving stiff higher-order ordinary differential equations are described. The convergence, zero stability and consistency of these methods are defined. Next, the zero stability and consistency conditions necessary for convergence are proven. The order for which the methods are zero stable is also determined.

Necessary and sufficient conditions for parameter convergence in adaptive control

-Using Generalized Harmonic Analysis, a complete description of parameter convergence in Model Reference Adaptive Control (MRAC) is given in terms of the spectrum of the exogenous reference input signal. Roughly speaking, if the reference signal "contains enough frequencies" then the parameter vector converges to its correct value. If not, it converges to an easily characterizable subspace in p...

Convergence of some random functionals of discretized semimartingales

In this paper, we study the asymptotic behavior of sums of functions of the increments of a given semimartingale, taken along a regular grid whose mesh goes to 0. The function of the ith increment may depend on the current time, and also on the past of the semimartingale before this time. We study the convergence in probability of two types of such sums, and we also give associated central limi...

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems