Showing papers in "Mathematische Nachrichten in 1985"
199 citations
TL;DR: In this article, an optimal stopping problem for a time-homogeneous, onedimensional, regular diffusion is considered, and the MARTIN boundary theory is used to determine explicitly the representing measure of a given β-excessive function.
Abstract: In this paper we consider an optimal stopping problem for a time-homogeneous, onedimensional, regular diffusion. An essential tool in our approach is the MARTIN boundary theory. It is possible to determine explicitly the representing measure of a given β-excessive function. It is seen that this correspondence may be used to construct optimal stopping rules. In some specific cases, as demonstrated in the paper, the solution is reached directly and with ease. The so called condition of “smooth pasting” is seen to be a simple consequence of our results.
129 citations
TL;DR: In this article, the authors present some results on quasivariational inequalities in topological linear locally convex Hausdorff spaces, where the compactness of the subset C is replaced by the condensing property of the mapping E. They also obtain some results for the multivalued mapping E maps C into 2X and satisfies a general inward boundary condition.
Abstract: This paper will present some results on quasivariational inequality {C, E, P, Φ} in topological linear locally convex Hausdorff spaces. We shall be concerning with quasivariational inequalities defined on subsets which are convexe closed, or only closed. The compactness of the subset C is replaced by the condensing property of the mapping E. Further, we also obtain some results for quasivariational inequality {C, E, P, Φ}, where the multivalued mapping E maps C into 2X and satisfies a general inward boundary condition.
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TL;DR: The notion of HEWITT-STROMBERG dimension of separable metric spaces is introduced and some first results are presented in this article, where the dimension is compared with the HAUSDORFF dimension and the metric dimension of separating metric spaces.
Abstract: The notion of HEWITT-STROMBERG dimension of separable metric spaces is introduced and some first results are presented. This dimension will be compared with the HAUSDORFF dimension and the metric dimension of separable metric spaces.
32 citations
TL;DR: In this article, it was shown that the solution of the heat equation with a two-parameter white GAUSSian noise can be approximated by solutions of this equation with physically real GAussian noise.
Abstract: We show under which conditions the solution of the heat equation with a two-parameter white GAUSSian noise can be approximated by solutions of this equation with physically real GAUSSian noise.
TL;DR: In this paper, a differentialgleichungssystem x′(t) = (B + t−1A) x(t), which is uber the LAPLACE-Transformation with parameterabhangigen Differential Gleichingsystem (s − B) v′(s) =(ρ − A) v(s), is gekoppelt.
Abstract: Das Differentialgleichungssystem x′(t) = (B + t−1A) x(t) ist uber die LAPLACE-Transformation mit dem parameterabhangigen Differentialgleichungssystem (s − B) v′(s) = (ρ − A) v(s) gekoppelt. In dieser Arbeit werden Losungen der Systeme untersucht, die an den Singularitaten t = ∞ bzw. s Eigenwert von B bzw. ρ = ∞ ein besonderes Verhalten haben. Es wird gezeigt, das mehrere Zusammenhangsrelationen zwischen solchen „lokalen” Losungen eng verknupft sind. Ein Hauptergebnis ist eine Grenzwertformel fur gewisse STOKESsche Koeffizienten des t-Systems.
TL;DR: The main theorem of as mentioned in this paper states that a graph has exactly two negative eigenvalues if and only if its canonical graph (defined below) is one of nine particular graphs on 3, 4, 5 and 6 vertices.
Abstract: In this paper we determine all finite connected graphs whose spectrum contains exactly two negative eigenvalues. The main theorem says that a graph has exactly two negative eigenvalues if and only if its “canonical graph” (defined below) is one of nine particular graphs on 3, 4, 5 and 6 vertices.
TL;DR: In this paper, an apriori bound for the arithmetical rank of monomial ideals is given, i.e., the minimal number of hypersurfaces which cut out set-theoretically the variety of such an ideal.
Abstract: In this paper we give an algorithm to compute an upper bound for the arithmetical rank of squarefree monomial ideals, i.e. the minimal number of hypersurfaces which cut out set-theoretically the variety of such an ideal. An apriori bound N – a=b+2 is obtained, where N means the number of variables, a the lowest degree in the ideal and b the lowest degree of syzygies in the first syzygy module (Thm. 2). These results sharpen more general results of [2] for the considered class of ideals by methods different from [1], [7].