Continuity and boundedness of infinitely divisible processes: a Poisson point process approach

Properties of Stationary Distributions of a Sequence of Generalized Ornstein–uhlenbeck Processes

The infinite (in both directions) sequence of the distributions μ of the stochastic integrals ∫∞− 0 c−N (k) t− dL (k) t for integers k is investigated. Here c > 1 and (N (k) t , L (k) t ), t ≥ 0, is a bivariate compound Poisson process with Lévy measure concentrated on three points (1, 0), (0, 1), (1, c−k). The amounts of the normalized Lévy measure at these points are denoted by p, q, r. For k...

Sufficient conditions for boundedness of moving average processes

We show that the moving average process Xf (t) := ∫ t 0 f(t − s) dZ(s) t ∈ [0, T ] has a bounded version almost surely, when the kernel f has finite total 2– variation and Z is a symmetric Lévy process. We also obtain bounds for E| supt∈[0,T ] Xf (t)| and for uniform moduli of continuity of Xf ( · ) and for the largest jump of Xf ( · ) when it is not continuous. Similar results are obtained for...

Markov Infinitely-Divisible Stationary Time-Reversible Integer-Valued Processes

We characterize all stationary time reversible Markov processes whose finite dimensional marginal distributions (of all orders) are infinitely divisible– MISTI processes, for short. Aside from two degenerate cases (iid and constant), in both discrete and continuous time every such process with full support is a branching process with Poisson or Negative Binomial marginal univariate distribution...

Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes

Drift Change Point Estimation in the rate and dependence Parameters of Autocorrelated Poisson Count Processes Using MLE Approach: An Application to IP Counts Data

Change point estimation in the area of statistical process control has received considerable attentions in the recent decades because it helps process engineer to identify and remove assignable causes as quickly as possible. On the other hand, improving in measurement systems and data storage, lead to taking observations very close to each other in time and as a result increasing autocorrelatio...