We study a particular class of moving average processes which possess a property called localisability. This means that, at any given point, they admit a “tangent process”, in a suitable sense. We give general conditions on the kernel g defining the moving average which ensures that the process is localisable and we characterize the nature of the associated tangent processes. Examples include t...

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...

This thesis introduces time-frequency-autoregressive-moving-average (TFARMA) models for underspread nonstationary stochastic processes (i.e., nonstationary processes with rapidly decaying TF correlations). TFARMAmodels are parsimonious as well as physically intuitive and meaningful because they are formulated in terms of time shifts (delays) and Doppler frequency shifts. They are a subclass of ...

In this paper we study the extremal behavior of a stationary continuoustime moving average process Y (t) = ∫∞ −∞ f(t−s) dL(s) for t ∈ R, where f is a deterministic function and L is a Lévy process whose increments, represented by L(1), are subexponential and in the maximum domain of attraction of the Gumbel distribution. We give necessary and sufficient conditions for Y to be a stationary, infi...

In this paper, the uncertain transition matrices for inhomogeneous Markov decision processes are described by use of fuzzy sets. Introducing a ν-step contractive property, called a minorization condition, for the average case, we fined a Pareto optimal policy maximizing the average expected fuzzy rewards under some partial order. The Pareto optimal policies are characterized by maximal solution...