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Uniqueness for stochastic evolution equations in Banach spaces

Martin Ondreját — 2004

Different types of uniqueness (e.g. pathwise uniqueness, uniqueness in law, joint uniqueness in law) and existence (e.g. strong solution, martingale solution) for stochastic evolution equations driven by a Wiener process are studied and compared. We show a sufficient condition for a joint distribution of a process and a Wiener process to be a solution of a given SPDE. Equivalences between different concepts of solution are shown. An alternative approach to the construction of the stochastic integral...

Towards one conjecture on collapsing of the Serre spectral sequence

Markl, Martin — 1990

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] A fibration F E B is called totally noncohomologuous to zero (TNCZ) with respect to the coefficient field k, if H * ( E ; k ) H * ( F ; k ) is surjective. This is equivalent to saying that π 1 ( B ) acts trivially on H * ( F ; k ) and the Serre spectral sequence collapses at E 2 . S. Halperin conjectured that for c h a r ( k ) = 0 and F a 1-connected rationally elliptic space (i.e., both H * ( F ; 𝒬 ) and π * ( F ) 𝒬 are finite dimensional) such that H * ( F ; k ) vanishes in odd degrees, every fibration F E B is TNCZ. The author proves this being the case...

A proof of the Baues-Lemaire conjecture in rational homotopy theory

Majewski, Martin — 1993

Proceedings of the Winter School "Geometry and Physics"

This paper contains an announcement of a result, which settles the connection between various algebraic models for rational homotopy theory: the models of Quillen, Sullivan and Adams-Hilton-Anick. It is shown how this result, combined with a recent result of Anick, implies a conjecture of and [Math. Ann. 225, 219-245 (1977; Zbl 0322.55019)].We describe in some detail the construction of these models (Section 1). We present a variant of the Adams-Hilton model, which is defined in a natural way...

Cells of harmonicity

Kolář, Martin — 1991

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]We are interested in partial differential equations on domains in 𝒞 n . One of the most natural questions is that of analytic continuation of solutions and domains of holomorphy. Our aim is to describe the domains of holomorphy for solutions of the complex Laplace and Dirac equations. We call them cells of harmonicity. We deduce their properties mostly by examining geometrical properties of the characteristic surface (which is the same for both equations),...

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