Relative smoothness—a notion introduced in Birnbaum et al. (Proceedings of the 12th ACM conference on electronic commerce, ACM, pp 127–136, 2011) and recently rediscovered Bauschke (Math Oper Res 330–348, 2016) Lu (Relatively-smooth convex optimization by first-order methods, applications, arXiv:1610.05708 , 2016)—generalizes standard smoothness typically used analysis gradient type methods. In...

Distributions of the first-exit times from a region with non-linear upper boundary are discussed for ordinary and compound Poisson processes. Explicit formulae are developed for the case of ordinary Poisson processes. Recursive formulae are given for the compound Poisson case, where the jumps are positive, having continuous distributions with finite means. Applications to sequential point estim...

The measurement and analysis of common recurrent conditions such as diarrhoea, respiratory infections or fever pose methodological challenges with regard to case definition, disease surveillance and statistical analysis. In this paper we describe a flexible and robust model that can generate simulated longitudinal datasets for a range of recurrent infections, reflecting the stochastic processes...

In recent years, implicit stochastic Runge–Kutta (SRK) methods have been developed both for strong and weak approximations. For these methods, the stage values are only given implicitly. However, in practice these implicit equations are solved by iterative schemes such as simple iteration, modified Newton iteration or full Newton iteration. We employ a unifying approach for the construction of ...

vii