scholarly journals Absolute Continuity of Measures Corresponding to Diffusion Processes in Banach Space

1973 ◽  
Vol 1 (3) ◽  
pp. 513-518 ◽  
Author(s):  
Hui-Hsiung Kuo
Keyword(s):  
Banach Space ◽  
Absolute Continuity ◽  
Diffusion Processes

FINITE DIMENSIONAL APPROXIMATIONS OF DIFFUSION PROCESSES ON BANACH SPACES

2001 ◽  
Vol 04 (04) ◽  
pp. 521-531
Author(s):  
T. S. ZHANG
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Quadratic Forms ◽  
Diffusion Processes ◽  
Existence Proof ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Dimensional Diffusion ◽  
Weak Limits

In this paper, we prove that the laws of diffusion processes on a Banach space X associated with quadratic forms (not necessarily symmetric) are the weak limits of laws of finite dimensional diffusions. A new existence proof for the infinite dimensional diffusion processes is obtained as a by-product.

scholarly journals Anosov diffeomorphisms, anisotropic BV spaces and regularity of foliations

2021 ◽  
pp. 1-37
Author(s):  
WAEL BAHSOUN ◽  
CARLANGELO LIVERANI
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Absolute Continuity ◽  
Hyperbolic Systems ◽  
Transfer Operator ◽  
Statistical Properties ◽  
Functions Of Bounded Variation ◽  
Expanding Maps ◽  
New Information ◽  
Piecewise Expanding Maps

Abstract Given any smooth Anosov map, we construct a Banach space on which the associated transfer operator is quasi-compact. The peculiarity of such a space is that, in the case of expanding maps, it reduces exactly to the usual space of functions of bounded variation which has proved to be particularly successful in studying the statistical properties of piecewise expanding maps. Our approach is based on a new method of studying the absolute continuity of foliations, which provides new information that could prove useful in treating hyperbolic systems with singularities.

Absolute continuity for Banach space valued mappings

2007 ◽  
Vol 56 (1) ◽  
pp. 116-124
Author(s):  
Cristina Di Bari ◽  
Calogero Vetro
Keyword(s):  
Banach Space ◽  
Absolute Continuity

DECOMPOSITIONS OF SPACES OF MEASURES

2008 ◽  
Vol 11 (01) ◽  
pp. 119-126
Author(s):  
IOANNIS ANTONIOU ◽  
COSTAS KARANIKAS ◽  
STANISLAV SHKARIN
Keyword(s):  
Banach Space ◽  
Absolute Continuity ◽  
Linear Subspace ◽  
Decomposition Theorem ◽  
Measurable Space ◽  
Jordan Decomposition ◽  
Closed Linear Subspace ◽  
Complex Valued ◽  
Spaces Of Measures ◽  
Nikodym Theorem

Let 𝔐 be the Banach space of σ-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of 𝔐 is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon–Nikodým theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen–Wintner purity theorem for our decompositions.

Meridional Circulation, Turbulence, and Diffusion Processes in Stars

1976 ◽  
Vol 32 ◽  
pp. 109-116 ◽  
Author(s):  
S. Vauclair
Keyword(s):  
Convection Zone ◽  
Diffusion Processes ◽  
Meridional Circulation ◽  
Diffusion Time ◽  
Work In Progress ◽  
First Results ◽  
Stellar Envelopes ◽  
And Diffusion ◽  
Turbulence And Diffusion ◽  
Hr Diagram

This paper gives the first results of a work in progress, in collaboration with G. Michaud and G. Vauclair. It is a first attempt to compute the effects of meridional circulation and turbulence on diffusion processes in stellar envelopes. Computations have been made for a 2 Mʘstar, which lies in the Am - δ Scuti region of the HR diagram.Let us recall that in Am stars diffusion cannot occur between the two outer convection zones, contrary to what was assumed by Watson (1970, 1971) and Smith (1971), since they are linked by overshooting (Latour, 1972; Toomre et al., 1975). But diffusion may occur at the bottom of the second convection zone. According to Vauclair et al. (1974), the second convection zone, due to He II ionization, disappears after a time equal to the helium diffusion time, and then diffusion may happen at the bottom of the first convection zone, so that the arguments by Watson and Smith are preserved.

Ergodic Control of Diffusion Processes

2009 ◽  
Author(s):  
Ari Arapostathis ◽  
Vivek S. Borkar ◽  
Mrinal K. Ghosh
Keyword(s):  
Diffusion Processes ◽  
Ergodic Control
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