Consider a particular bidimensional risk model, in which two insurance companies divide between them in different proportions both the premium income and the aggregate claims. In practice, it can be interpreted as an insurer–reinsurer scenario, where the reinsurer takes over a proportion of the insurer's losses. Under the assumption that the claim sizes and inter-arrival times form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure, an asymptotic expression for the ruin probability of this bidimensional risk model with constant interest rates is established.

A novel strain-rate jump method was developed for the plane-strain bulge test and used to investigate the time-dependent deformation behavior of gold thin films in the thickness range 100–400 nm. The experimental method is based on an abrupt variation of the pressurization rate. The evaluated strain-rate sensitivity was found to be five times higher for films in freestanding condition (m = 0.094) than for films tested on a SiNx substrate (m = 0.020). Bulge creep tests confirmed this increased time-dependence. The observation of the surface of the freestanding films after the creep tests provided evidence of apparent grain boundary sliding taking place next to intragranular plastic deformation. The out-of-plane deformation was presumably favored by the columnar microstructure of the samples, with grains extending between both free surfaces. In the case of SiNx-supported films, grain boundary sliding was prevented by the good adhesion of gold to the SiNx substrate.

A distributional coupling concept is defined for continuous-time stochastic processes on a general state space and applied to processes having a certain non-time-homogeneous regeneration property: regeneration occurs at random times So, S1, · ·· forming an increasing Markov chain, the post-Sn process is conditionally independent of So, · ··, Sn–1 given Sn, and the conditional distribution is independent of n. The coupling problem is reduced to an investigation of the regeneration times So, S1, · ··, and a successful coupling is constructed under the condition that the recurrence times Xn+1 = Sn+1 – Sn given that , are stochastically dominated by an integrable random variable, and that the distributions , have a common component which is absolutely continuous with respect to Lebesgue measure (or aperiodic when the Sn's are lattice-valued). This yields results on the tendency to forget initial conditions as time tends to ∞. In particular, tendency towards equilibrium is obtained, provided the post-Sn process is independent of Sn. The ergodic results cover convergence and uniform convergence of distributions and mean measures in total variation norm. Rate results are also obtained under moment conditions on the Ps's and the times of the first regeneration.