On boundedness of stochastic sequences and estimates of their moments (Q1972642)

Let \(X_n\), \(n=0,1,\dots \), be a random process on \({\mathbb R}^+\). In the first section, the known submartingale-type conditions for ``positive recurrence'' are relaxed. Conditions are also given under which \(\{ X_n\}\) is bounded in distribution. In the second section, similar estimates are presented for the exponential moments of \(X_n\). The boundedness problem for moments of \(X_n\) is studied in the third section.