We give a personal (and we hope, not too idiosyncratic) view of how our subject of probability theory has developed during the last half-century, and the author in tandem with it.

We survey some aspects of the classical prediction theory for stationary processes, in discrete time in Section 1, turning in Section 2 to continuous time, with particular reference to reproducing-kernel Hilbert spaces and the sampling theorem. We discuss the discrete-continuous theories of ARMA-CARMA, GARCH-COGARCH, and OPUC-COPUC in Section 3. We compare the various models treated in Section 4 by how well they model volatility, in particular volatility clustering. We discuss the infinite-dimensional case in Section 5, and turn briefly to applications in Section 6.

Forcing by steep regular water waves on a vertical circular cylinder at finite depth was investigated numerically by solving the two-phase incompressible Navier–Stokes equations. Consistently with potential flow theory, boundary layer effects were neglected at the sea bed and at the cylinder surface, but the strong nonlinear motion of the free surface was included. The numerical model was verified and validated by grid convergence and by comparison to relevant experimental measurements. First-order convergence towards an analytical solution was demonstrated and an excellent agreement with the experimental data was found. Time-domain computations of the normalized inline force history on the cylinder were analysed as a function of dimensionless wave height, water depth and wavelength. Here the dependence on depth was weak, while an increase in wavelength or wave height both lead to the formation of secondary load cycles. Special attention was paid to this secondary load cycle and the flow features that cause it. By visual observation and a simplified analytical model it was shown that the secondary load cycle was caused by the strong nonlinear motion of the free surface which drives a return flow at the back of the cylinder following the passage of the wave crest. The numerical computations were further analysed in the frequency domain. For a representative example, the secondary load cycle was found to be associated with frequencies above the fifth- and sixth-harmonic force component. For the third-harmonic force, a good agreement with the perturbation theories of Faltinsen, Newman & Vinje (J. Fluid Mech., vol. 289, 1995, pp. 179–198) and Malenica & Molin (J. Fluid Mech., vol. 302, 1995, pp. 203–229) was found. It was shown that the third-harmonic forces were estimated well by a Morison force formulation in deep water but start to deviate at decreasing depth.

Offspring of diabetic mothers experience an increased risk for type 2 diabetes but it is not known whether diabetic pregnancies also confer a higher inter-generational risk for diabetic complications. Because microalbuminuria is a sensitive indicator of glomerular damage, we compared the urine albumin:creatinine ratios (ACRs) between 65 infants of diabetic mothers (InfDM+) and 59 infants of non-diabetic mothers (InfDM−), and repeated the comparisons in 21 InfDM+ and 19 InfDM− when children were 5–19 months old. ACRs were higher among neonates compared with normal reference values for adults, but declined with increasing age. The only independent predictor of higher ACRs in a logistic regression model (⩾13 mg/mmol v. <13 mg/mmol) was the presence of delivery complications (odds ratio 2.95; P = 0.015). Neither high nor low birth weight was associated with higher neonatal ACRs. The most unique finding of the study was that InfDM+ had significantly lower ACRs than InfDM− [mean = 12.9 (median = 6.0) v. mean = 16.6 (median = 11.5), respectively at P = 0.05] even after adjusting for other variables using logistic regression (odds ratio 0.25; P = 0.001). In contrast, by 5–19 months, there was a trend toward higher ACRs among InfDM+ compared with InfDM− [mean = 6.3 mg/mmol (median = 1.9) v. mean = 3.0 mg/mmol (median = 2.5), respectively at P = 0.25]. Lower ACRs in InfDM+ may be due to developmental changes in fetal kidneys induced by hyperinsulinemia. Although the implications of this observation are unclear, it is possible that exposure to a diabetic intrauterine environment might influence the later risk for renal disease.

The Kestelman–Borwein–Ditor Theorem, on embedding a null sequence by translation in (measure/category) “large” sets has two generalizations. Miller replaces the translated sequence by a “sequence homotopic to the identity”. The authors, in a previous paper, replace points by functions: a uniform functional null sequence replaces the null sequence, and translation receives a functional form. We give a unified approach to results of this kind. In particular, we show that (i) Miller's homotopy version follows fromthe functional version, and (ii) the pointwise instance of the functional version follows from Miller's homotopy version.

We define combinatorial principles which unify and extend the classical results of Steinhaus and Piccard on the existence of interior points in the distance set. Thus the measure and category versions are derived from one topological theorem on interior points applied to the usual topology and the density topology on the line. Likewise we unify the subgroup theorem by reference to a Ramsey property. A combinatorial form of Ostrowski's theorem (that a bounded additive function is linear) permits the deduction of both the measure and category automatic continuity theorems for additive functions.