Sufficient Conditions for Boundedness of Moving Average Processes

We show that the moving average process Χ_f(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| sup t#[0,T ] f (t)| and for uniform moduli of continuity of Χ_f(·) and for the largest jump of Χ_f(·) when it is not continuous. Similar results are obtained for forward average processes. The methods developed are also used to show that certain infinitely divisible random fields are bounded