On recurrence property of Riesz-Raikov sums.
We present a general method for the extension of results about linear prediction for q-variate weakly stationary processes on a separable locally compact abelian group (whose dual is a Polish space) with known values of the processes on a separable subset to results for weakly stationary processes on with observed values on . In particular, the method is applied to obtain new proofs of some well-known results of Ze Pei Jiang.
In this paper, we consider the linear and circular consecutive -out-of- systems consisting of arbitrarily dependent components. Under the condition that at least components () of the system are working at time , we study the reliability properties of the residual lifetime of such systems. Also, we present some stochastic ordering properties of residual lifetime of consecutive -out-of- systems. In the following, we investigate the inactivity time of the component with lifetime at the system...
We give some criteria for mutual absolute continuity and for singularity of Riesz product measures on locally compact abelian groups. The first section gives the definition of such a measure which is more general than the usual definition. The second section provides three sufficient conditions for one Riesz product measure to be absolutely continuous with respect to another. One of our results contains a theorem of Brown-Moran-Ritter as a special case. The final section deals with random Riesz...
The purpose of this work is a study of the following insurance reserve model: , t ∈ [0,T], P(η ≥ c) ≥ 1-ϵ, ϵ ≥ 0. Under viability-type assumptions on a pair (p,σ) the estimation γ with the property: is considered.
Risk-sensitive control problem of regular step Markov processes is considered, firstly when the control parameters are changed at shift times and then in the general case.