Consider events of the form {Zs=[zeta](s),s[set membership, variant]S}, where Z is a continuous Gaussian process with stationary increments, [zeta] is a function that belongs to the reproducing kernel Hilbert space R of process Z, and is compact. The main problem considered in this paper is...

Let [sigma](t,t') be the sigma-algebra generated by the differences Xs-Xs' with s,s'[set membership, variant](t,t'), where (Xt)-[infinity]t[infinity] is the fractional Brownian motion with Hurst index H[set membership, variant](0,1). We prove that for any two distinct timepoints t1 and t2 the...

The ideas of a dynamic approach to the analysis of multivariate life length distributions, introduced in Arjas (1981a) and Arjas and Norros (1984), are developed further. Basic definitions are given in terms of prediction processes. Properties of martingales jumping downwards at failure times...