Continuity of sample functions of biadditive processes

W. N. Hudson

Vol. 42 (1972), No. 2, 343–358

DOI: 10.2140/pjm.1972.42.343

Abstract

Let {X(s,t) : 0 ≦ s,t ≦ 1} be a stochastic process which has independent increments (second differences). Necessary and sufficient conditions are established to ensure the existence of a version with the property that almost every sample function is continuous. A corollary to these results is the existence of a class of measures on Wiener-Yeh space. The conditions are analogous to the usual case of additive processes Z(t) indexed by one time parameter.

Mathematical Subject Classification 2000

Primary: 60J30

Secondary: 60G15, 60G17

Milestones

Received: 29 April 1971

Published: 1 August 1972