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Most random walks on nilpotent groups are mixing

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Rębowski R.

Annales Polonici Mathematici

1992

tom 57

nr 3

265-268

Let G be a second countable locally compact nilpotent group. It is shown that for every norm completely mixing (n.c.m.) random walk μ, αμ + (1-α)ν is n.c.m. for 0 < α ≤ 1, ν ∈ P(G). In particular, a generic stochastic convolution operator on G is n.c.m.

A note on integral representation of Feller kernels

100%

Rębowski R.

Annales Polonici Mathematici

1991-1992

tom 56

nr 1

93-96

We consider integral representations of Feller probability kernels from a Tikhonov space X into a Hausdorff space Y by continuous functions from X into Y. From the existence of such a representation for every kernel it follows that the space X has to be 0-dimensional. Moreover, both types of representations coincide in the metrizable case when in addition X is compact and Y is complete. It is also proved that the representation of a single kernel is equivalent to the existence of some non-direct product measure on the product space $Y^ℕ$.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Rębowski R.

1 1992

1 1991

Wyniki wyszukiwania

Most random walks on nilpotent groups are mixing

A note on integral representation of Feller kernels