LIMIT-THEOREMS OF HILBERT VALUED SEMIMARTINGALES AND HILBERT VALUED MARTINGALE MEASURES

In this paper, we study tight criteria of cadlag Hilbert valued proces ses and prove the tightness of Hilbert valued square integrable martin gales and Hilbert valued semimartingales by using their characteristic s. These extend appropriate results of Jacod and Shiryaev (1987). We a lso discuss the property of Hilbert valued martingale measure and intr oduce the concept of convergence of martingale measures in distributio n. The sufficient and necessary conditions are provided for strongly o rthogonal martingale measures with independent increments. The conditi ons are given for convergence of martingale measures.