THIS SUPPLEMENTAL MATERIAL contains the proofs of all the lemmas that do not appear in the printed Appendix to the paper. It also contains the statements of all these lemmas and details of the intervening arguments in the proofs of the propositions. These arguments appeared in the printed Appendix. It also contains a proof of existence for a more general model that implies Proposition 3(ii). Th...

We study the nonlinear stochastic heat equation driven by spacetime white noise in the case that the initial datum u0 is a (possibly signed) measure. In this case, one cannot obtain a mild random-field solution in the usual sense. We prove instead that it is possible to establish the existence and uniqueness of a weak solution with values in a suitable function space. Our approach is based on a...

In this article we give sufficient and necessary conditions for the existence of a weak mild solution to stochastic evolution equations with (general) Lévy noise taking values in dual nuclear space. As part our approach develop theory integration respect process We also derive further properties such as square moments, Markov property path regularity solution. final paper convergence solutions ...

We are interested in path-dependent semilinear PDEs, where the derivatives of Gâteaux type specific directions [Formula: see text] and text], being kernel functions a Volterra Gaussian process text]. Under some conditions on coefficients PDE, we prove existence uniqueness decoupled mild solution, notion introduced previous paper by authors. also show that solution PDE can be represented through...

Entropy Methods for Identifying Hedonic Models This paper contributes to the literature on hedonic models in two ways. First, it makes use of Queyranne’s reformulation of a hedonic model in the discrete case as a network flow problem in order to provide a proof of existence and integrality of a hedonic equilibrium and efficient computational techniques of hedonic prices. Second, elaborating on ...

In 2002, a method has been proposed by Buchholz et al. in the context of Local Quantum Physics, to characterize states that are locally in thermodynamic equilibrium. It could be shown for the model of massless bosons that these states exhibit quite interesting properties. The mean phase-space density satisfies a transport equation, and many of these states break time reversal symmetry. Moreover...

We give a concise definition of mitered offset surfaces for nonconvex polytopes in R, along with a proof of existence and a discussion of basic properties. These results imply the existence of 3D straight skeletons for general nonconvex polytopes. The geometric, topological, and algorithmic features of such skeletons are investigated, including a classification of their constructing events in t...

We apply the well-known Banach-Nečas-Babuška inf-sup theory in a stochastic setting to introduce a weak space-time formulation of the linear stochastic heat equation with additive noise. We give sufficient conditions on the the data and on the covariance operator associated to the driving Wiener process, in order to have existence and uniqueness of the solution. We show the relation of the obta...

We consider the stationary flow of a heat conducting Power Law shear thinning fluid in a bounded domain in R2. We present an elementary proof of existence of at least one weak solution.