Convolution Semigroups Of Measures Research Articles

Limit Theorems for a Storage Process with a Random Release Rule

We consider a discrete time Storage Process Xn with a simple random walk input Sn and a random release rule given by a family {Ux, x ≥ 0} of random variables whose probability laws {Ux, x ≥ 0} form a convolution semigroup of measures, that is, μx × μy = μx + y The process Xn obeys the equation: X0 = 0, U0 = 0, Xn = Sn － USn, n ≥ 1. Under mild assumptions, we prove that the processes and are simple random walks and derive a SLLN and a CLT for each of them.

Criteria for analyticity of subordinate semigroups

Let ψ be a Bernstein function. A. Carasso and T. Kato obtained necessary and sufficient conditions for ψ to have the property that ψ(A) generates a quasibounded holomorphic semigroup for every generator A of a bounded C0-semigroup in a Banach space, in terms of some convolution semigroup of measures associated with ψ. We give an alternative to Carasso-Kato’s criterion, and derive several sufficient conditions for ψ to have the above-mentioned property.

Zero-One Law for Symmetric Convolution Semigroups of Measures on Groups

Let (μ t ) t>0 be a symmetric weakly continuous semigroup of probability measures on a nonabelien complete separable group G and let v be its Levy measure. The purpose of this paper is to provide a relatively simple proof of the zero-one law for semigroups with the Levy measure satisfying either v(H c) = ∞ or v(H c) = 0.

Semigroups of measures in non-commutative harmonic analysis

We find the invariant convolution semigroups of measures on the Heisenberg group which are analogous to the familiar semigroups in the abelian context from modern potential theory, and we show that the abelian theory may be obtained as the limit of the Heisenberg case as Planck's constant tends to zero.

On local integrability and transience of convolution semigroups of measures

The analytic proof due to M. Ito of the Kesten-Ornstein transience criterion for continuous convolution semigroups of nonnegative contraction measures on a compactly generated Abelian locally compact group has been reworked and given a self-contained form. The new proof still relies on the existence of the equilibrium measure but dispenses with the complete maximum principle.

Convolution semigroup of measures on compact noncommutative semigroups

Convolution semigroup of measures on compact noncommutative semigroups

Convolution semigroups of measures

Convolution semigroups of measures