Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t distributed measurement noise are presented. The proposed algorithms improve upon our earlier proposed filter and smoother using the mean field variational Bayes approximation of the posterior distribution to a skew-t likelihood and normal prior. Our simulations show that the proposed variational Bayes ap...

• In this paper, we introduce a generalized skew logistic distribution that contains the usual skew logistic distribution as a special case. Several mathematical properties of the distribution are discussed like the cumulative distribution function and moments. Furthermore, estimation using the method of maximum likelihood and the Fisher information matrix are investigated. Two real data applic...

A generalized Mehler semigroup (Ornstein-Uhlenbeck semigroup) associated with some strongly continuous semigroup of linear operators on a real separable Hilbert space may be defined by using a skew convolution semigroup. Under a mild moment assumption, it is proved that the characteristic functional of any centered skew convolution semigroup is absolutely continuous and characterizations are gi...

Skew convolution semigroups play an important role in the study of generalized Mehler semigroups and Ornstein-Uhlenbeck processes. We give a characterization for a general skew convolution semigroup on real separable Hilbert space whose characteristic functional is not necessarily differentiable at the initial time. A connection between this subject and catalytic branching superprocesses is est...

In this paper, we further investigate the local Hermitian and skew-Hermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. When A is non-symmetric positive definite, the convergence conditions are obtained, which generalize some results of Jiang and Cao [M.-Q. Jiang and Y. Ca...

In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynom...