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(Homogeneous) markovian bridges

Vincent Vigon (2011)

Annales de l'I.H.P. Probabilités et statistiques

(Homogeneous) Markov bridges are (time homogeneous) Markov chains which begin at a given point and end at a given point. The price to pay for preserving the homogeneity is to work with processes with a random life-span. Bridges are studied both for themselves and for their use in describing the transformations of Markov chains: restriction on a random interval, time reversal, time change, various conditionings comprising the confinement in some part of the state space. These bridges lead us to look...

Homomorphisms from the unitary group to the general linear group over complex number field and applications

Chong-Guang Cao, Xian Zhang (2002)

Archivum Mathematicum

Let M n be the multiplicative semigroup of all n × n complex matrices, and let U n and G L n be the n –degree unitary group and general linear group over complex number field, respectively. We characterize group homomorphisms from U n to G L m when n > m 1 or n = m 3 , and thereby determine multiplicative homomorphisms from U n to M m when n > m 1 or n = m 3 . This generalize Hochwald’s result in [Lin. Alg. Appl.  212/213:339-351(1994)]: if f : U n M n is a spectrum–preserving multiplicative homomorphism, then there exists a matrix R in G L n such that f ( A ) = R A R for...

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