In this paper, a general class of linear stochastic degenerate Sobolev equations with additive noise is considered. This class of systems is the infinite dimensional analogue of linear descriptor systems in finite dimensions. Under appropriate assumptions, the mild and strong well posedness for the initial value problem are studied using elements of the semigroup theory and properties of the stochastic convolution. The final value problem is also examined and it is proved that this is uniquely strongly solvable and the solution is continuously dependent on the final data. Based on the results of the forward and backward problem, the conditions for the exact controllability are investigated for a special but important class of these equations. The abstract results are illustrated by applications in complex media electromagnetics, in the one dimensional stochastic Dirac equation in the non-relativistic limit and in a potential application in input-output analysis in economics.

No abstract

No abstract

No abstract

We study the preventive maintenance scheduling problem of wind farms in the offshore wind energy sector which operates under uncertainty due to the state of the ocean and market demand. We formulate a fuzzy multi-objective non-linear chance-constrained programming model with newlydefined reliability and cost criteria and constraints to obtain satisfying schedules for wind turbine maintenance. To solve the optimization model, a 2-phase solution framework integrating the operational law for fuzzy arithmetic and the non-dominated sorting genetic algorithm II for multiobjective programming is developed. Pareto-optimal solutions of the schedules are obtained to form the trade-offs between the reliability maximization and cost minimization objectives. A numerical example is illustrated to validate the model.

No abstract

Temperature changes are known to affect the social and environmental determinants of health in various ways. Consequently, excess deaths as a result of extreme weather conditions may increase over the coming decades because of climate change. In this paper, the relationship between trends in mortality and trends in temperature change (as a proxy) is investigated using annual data and for specified (warm and cold) periods during the year in the UK. A thoughtful statistical analysis is implemented and a new stochastic, central mortality rate model is proposed. The new model encompasses the good features of the Lee and Carter (Journal of the American Statistical Association, 1992, 87: 659–671) model and its recent extensions, and for the very first time includes an exogenous factor which is a temperature‐related factor. The new model is shown to provide a significantly better‐fitting performance and more interpretable forecasts. An illustrative example of pricing a life insurance product is provided and discussed.

In this paper, we revisit the recently proposed results for a general class of linear stochastic degenerate Sobolev systems with additive noise by using a different approach keeping, however, the main assumptions unchanged for the purpose of comparison. In particular, the mild and strong well‐posedness for the initial and final value problems are presented and studied by applying a suitable transformation that formulates the degenerate stochastic system as a pseudoparabolic one. Based on the derived results for the forward and backward cases, under this new framework, the conditions for the exact controllability are revisited for a particular class of degenerate Sobolev systems. Copyright © 2016 John Wiley & Sons, Ltd.