Stabilization and Random Linear Regulator Problem for Random Linear Control Processes

Laws of Large Numbers for Random Linear

The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...

Linear Phase Transition in Random Linear Constraint Satisfaction Problem

Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints C on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and a constraint is chosen from C also uniformly at random. This procedure is repeated m times independently. We ask the following question: is the resulting li...

Linear Wavelet-Based Estimation for Derivative of a Density under Random Censorship

In this paper we consider estimation of the derivative of a density based on wavelets methods using randomly right censored data. We extend the results regarding the asymptotic convergence rates due to Prakasa Rao (1996) and Chaubey et al. (2008) under random censorship model. Our treatment is facilitated by results of Stute (1995) and Li (2003) that enable us in demonstrating that the same con...

Random linear embeddings

This lemma states that any finite point set can be linearly embedded into Rk such that all pairwise distances are approximately preserved. What is remarkable is that the required target dimension k does not depend on the source dimension d at all. Therefore, any data analysis that depends only on interpoint Euclidean distances between n data points can be approximately carried out in dimension ...

Random linear maps