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This paper provides expressions for solutions of a one-dimensional global optimization problem using an adjoint variable which represents the available one-sided improvements up to the interval "horizon." Interpreting the problem in terms of optimal stoppi ...
Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations involving fractional Brownian motions and, as such, their exact value is often unknown. Recently, D ...
Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In applications, an assu ...
We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...
Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect depen ...
We study frictionless and non-adhesive contact between elastic half-spaces with self-affine surfaces. Using a recently suggested corrective technique, we ensure an unprecedented accuracy in computation of the true contact area evolution under increasing pr ...
In a recent article [1] we surveyed advances related to adaptation, learning, and optimization over synchronous networks. Various distributed strategies were discussed that enable a collection of networked agents to interact locally in response to streamin ...
Most current risk assessment for complex extreme events relies on catalogues of similar events, either historical or generated artificially. In the latter, no existing methods produce completely new events with mathematically justified extrapolation above ...
Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...
We study the optimal strategy for a sailboat to reach an upwind island under the hypothesis that the wind direction fluctuates according to a Brownian motion and the wind speed is constant. The work is motivated by a concrete problem which typically arises ...