Absolute Continuity Under Time Shift Of Trajectories And Related Stochastic Calculus
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Absolute Continuity Under Time Shift Of Trajectories And Related Stochastic Calculus
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Author : Jörg-Uwe Löbus
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-09-25
Absolute Continuity Under Time Shift Of Trajectories And Related Stochastic Calculus written by Jörg-Uwe Löbus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-25 with Mathematics categories.
The text is concerned with a class of two-sided stochastic processes of the form . Here is a two-sided Brownian motion with random initial data at time zero and is a function of . Elements of the related stochastic calculus are introduced. In particular, the calculus is adjusted to the case when is a jump process. Absolute continuity of under time shift of trajectories is investigated. For example under various conditions on the initial density with respect to the Lebesgue measure, , and on with we verify i.e. where the product is taken over all coordinates. Here is the divergence of with respect to the initial position. Crucial for this is the temporal homogeneity of in the sense that , , where is the trajectory taking the constant value . By means of such a density, partial integration relative to a generator type operator of the process is established. Relative compactness of sequences of such processes is established.
Absolute Continuity Under Time Shift Of Trajectories And Related Stochastic Calculus
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Author : Jörg-Uwe Löbus
language : en
Publisher:
Release Date : 2017
Absolute Continuity Under Time Shift Of Trajectories And Related Stochastic Calculus written by Jörg-Uwe Löbus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with MATHEMATICS categories.
The text is concerned with a class of two-sided stochastic processes of the form X=W+A. Here W is a two-sided Brownian motion with random initial data at time zero and A\equiv A(W) is a function of W. Elements of the related stochastic calculus are introduced. In particular, the calculus is adjusted to the case when A is a jump process. Absolute continuity of (X,P) under time shift of trajectories is investigated. For example under various conditions on the initial density with respect to the Lebesgue measure, m, and on A with A_0=0 we verify \frac{P(dX_{\cdot -t})}{P(dX_\cdot)}=\frac{m(X_{-t}
Mathematical Study Of Degenerate Boundary Layers A Large Scale Ocean Circulation Problem
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Author : Anne-Laure Dalibard
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Mathematical Study Of Degenerate Boundary Layers A Large Scale Ocean Circulation Problem written by Anne-Laure Dalibard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
This paper is concerned with a complete asymptotic analysis as $E \to 0$ of the Munk equation $\partial _x\psi -E \Delta ^2 \psi = \tau $ in a domain $\Omega \subset \mathbf R^2$, supplemented with boundary conditions for $\psi $ and $\partial _n \psi $. This equation is a simple model for the circulation of currents in closed basins, the variables $x$ and $y$ being respectively the longitude and the latitude. A crude analysis shows that as $E \to 0$, the weak limit of $\psi $ satisfies the so-called Sverdrup transport equation inside the domain, namely $\partial _x \psi ^0=\tau $, while boundary layers appear in the vicinity of the boundary.
Globally Generated Vector Bundles With Small C 1 On Projective Spaces
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Author : Cristian Anghel
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Globally Generated Vector Bundles With Small C 1 On Projective Spaces written by Cristian Anghel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
The authors provide a complete classification of globally generated vector bundles with first Chern class $c_1 \leq 5$ one the projective plane and with $c_1 \leq 4$ on the projective $n$-space for $n \geq 3$. This reproves and extends, in a systematic manner, previous results obtained for $c_1 \leq 2$ by Sierra and Ugaglia [J. Pure Appl. Algebra 213 (2009), 2141-2146], and for $c_1 = 3$ by Anghel and Manolache [Math. Nachr. 286 (2013), 1407-1423] and, independently, by Sierra and Ugaglia [J. Pure Appl. Algebra 218 (2014), 174-180]. It turns out that the case $c_1 = 4$ is much more involved than the previous cases, especially on the projective 3-space. Among the bundles appearing in our classification one can find the Sasakura rank 3 vector bundle on the projective 4-space (conveniently twisted). The authors also propose a conjecture concerning the classification of globally generated vector bundles with $c_1 \leq n - 1$ on the projective $n$-space. They verify the conjecture for $n \leq 5$.
Degree Spectra Of Relations On A Cone
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Author : Matthew Harrison-Trainor
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Degree Spectra Of Relations On A Cone written by Matthew Harrison-Trainor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
Let $\mathcal A$ be a mathematical structure with an additional relation $R$. The author is interested in the degree spectrum of $R$, either among computable copies of $\mathcal A$ when $(\mathcal A,R)$ is a ``natural'' structure, or (to make this rigorous) among copies of $(\mathcal A,R)$ computable in a large degree d. He introduces the partial order of degree spectra on a cone and begin the study of these objects. Using a result of Harizanov--that, assuming an effectiveness condition on $\mathcal A$ and $R$, if $R$ is not intrinsically computable, then its degree spectrum contains all c.e. degrees--the author shows that there is a minimal non-trivial degree spectrum on a cone, consisting of the c.e. degrees.
Elliptic Pdes On Compact Ricci Limit Spaces And Applications
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Author : Shouhei Honda
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Elliptic Pdes On Compact Ricci Limit Spaces And Applications written by Shouhei Honda and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
In this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.
Neckpinch Dynamics For Asymmetric Surfaces Evolving By Mean Curvature Flow
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Author : Zhou Gang
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Neckpinch Dynamics For Asymmetric Surfaces Evolving By Mean Curvature Flow written by Zhou Gang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
The authors study noncompact surfaces evolving by mean curvature flow (mcf). For an open set of initial data that are $C^3$-close to round, but without assuming rotational symmetry or positive mean curvature, the authors show that mcf solutions become singular in finite time by forming neckpinches, and they obtain detailed asymptotics of that singularity formation. The results show in a precise way that mcf solutions become asymptotically rotationally symmetric near a neckpinch singularity.
Holomorphic Automorphic Forms And Cohomology
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Author : Roelof Bruggeman
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Holomorphic Automorphic Forms And Cohomology written by Roelof Bruggeman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
From Vertex Operator Algebras To Conformal Nets And Back
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Author : Sebastiano Carpi
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-09
From Vertex Operator Algebras To Conformal Nets And Back written by Sebastiano Carpi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-09 with Mathematics categories.
The authors consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. They present a general procedure which associates to every strongly local vertex operator algebra V a conformal net AV acting on the Hilbert space completion of V and prove that the isomorphism class of AV does not depend on the choice of the scalar product on V. They show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex operator algebra V, the map W↦AW gives a one-to-one correspondence between the unitary subalgebras W of V and the covariant subnets of AV.
Boundary Conditions And Subelliptic Estimates For Geometric Kramers Fokker Planck Operators On Manifolds With Boundaries
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Author : Francis Nier
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-03-19
Boundary Conditions And Subelliptic Estimates For Geometric Kramers Fokker Planck Operators On Manifolds With Boundaries written by Francis Nier and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with Mathematics categories.
This article is concerned with the maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible boundary conditions cover a wide range of applications for the usual scalar Kramer-Fokker-Planck equation or Bismut's hypoelliptic laplacian.