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Finite partitions of topological groups into congruent thick subsets

Weber H., Zoli E.

Journal of Applied Analysis

2008

Vol. 14, nr 1

1-12

We establish fairly general sufficient conditions for a locally compact group (a Baire topological group) to admit partitions into finitely many congruent μ-thick (everywhere of second category) subset.

Nonlinear singular integrals depending on two parametres

Świderski T., Wachnicki E.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2000

[Z] 40

181-189

Martingale characterizations of stochastic processes on compact groups

Voit M.

Probability and Mathematical Statistics

1999

Vol. 19, Fasc. 2

389--405

By a classical result of P. Lévy, the Brownian motion (Bt)t≥0 on R may be characterized as a continuous process on R such that (Bt)t≥0 and (B2t - t)t≥0 are martingales. Generalizations of this result are usually obtained in the setting of the so-called martingale problem. This paper contains a variant of the martingale problem for stochastic processes on locally compact groups with independent stationary increments that is based on irreducible unitary representations. In particular, for Gaussian processes on compact Lie groups, analogues of the Lévy-characterization above are obtained. It turns out that for certain compact Lie groups even the continuity assumption in this characterization can be dropped.