Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating correlations, Liapunov exponents and impact of noises, are discussed. They are relevant for understanding predictability in spatially extended systems with model uncer...

We give an abstract axiomatic account of timed processes using monoids and their (partial and total) actions. Subsequently, we present categorical formulations thereof, including a novel characterisation of partial monoid actions as coalgebras for an evolution comonad. Adapting the approach of Turi and Plotkin [24], we then exhibit an abstract theory of well-behaved operational rules suitable f...

The aim of this note is to emphasize the fact, not observed previously in the literature, that many discrepancy measures used in tests related to different stochastic orders can be expressed as expectations of order statistics. In this way, we provide a new meaning to the corresponding test statistics which allows us to understand better, and potentially improve, the testing procedures. As illu...

In the functional regression model where the responses are curves new tests for the functional form of the regression and the variance function are proposed, which are based on a stochastic process estimating L2-distances. Our approach avoids the explicit estimation of the functional regression and it is shown that normalized versions of the proposed test statistics converge weakly. The finite ...

Recently, several researchers have demonstrated domains where partially-ordered planners outperform totally-ordered planners. In (Barrett & Weld 1994), Barrett and Weld build a series of arti cial domains exploring the concepts of trivial and laborious serializability, in which a partially-ordered planner, snlp, consistently outperforms two totally-ordered planners. In this paper, we demonstrat...

Changes in climatic and policy environments combined with uncertainty related to stochastic environmental fluctuations make design of invasive pest policy challenging. These external changes are often exacerbated by changes in the species characteristics. We discuss facing local change and uncertainty when deciding ex ante on a specific policy strategy. Our empirical case deals with an invasive...

First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored due to the high cost of computing the second-order information. In this paper we develop second-order stochastic methods for optimization problems in machine ...

Let Pλ := Pλκ denote a Poisson point process of intensity λκ on [0,1]d , d ≥ 2, with κ a bounded density on [0,1]d and λ ∈ (0,∞). Given a closed subset M⊂ [0,1]d of Hausdorff dimension (d−1), we consider general statistics ∑ x∈Pλ ξ(x,Pλ,M), where the score function ξ vanishes unless the input x is close to M and where ξ satisfies a weak spatial dependency condition. We give a rate of normal con...

First-order approximation techniques for estimating stochastic parameters of a sediment transport model are presented. The non-homogeneous compound Poisson model of Shen-Todorovic eliminating certain idealized assumptions to describe the movement of sediment in natural streams is a revision of the earlier homogeneous model of Einstein-Hubbell-Sayre. However, the complexity of the non-homogeneou...

This paper discusses analytical and numerical issues related to elliptic equations with random coefficients which are generally nonlinear functions of white noise. Singularity issues are avoided by using the Itô-Skorohod calculus to interpret the interactions between the coefficients and the solution. The solution is constructed by means of theWiener Chaos (Cameron-Martin) expansions. The exist...