Displaying similar documents to “Scaling laws for non-euclidean plates and the W 2 , 2 isometric immersions of riemannian metrics”

Optional splitting formula in a progressively enlarged filtration

Shiqi Song (2014)

ESAIM: Probability and Statistics

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Let 𝔽 F be a filtration andbe a random time. Let 𝔾 G be the progressive enlargement of 𝔽 F with. We study the following formula, called the optional splitting formula: For any 𝔾 G-optional process, there exists an 𝔽 F-optional process and a function defined on [0∞] × (ℝ × ) being ℬ [ 0 , ∞ ] ⊗ 𝒪 ( 𝔽 ) ℬ[0,∞]⊗x1d4aa;(F) measurable, such that Y = Y ' 1 [ 0 , τ ) + Y ' ' ( τ ) 1 [ τ , ∞ ) . Y=Y′1[0,τ)+Y′′(τ)1[τ,∞). (This formula can also be formulated for multiple random times ...

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

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Let (Ω, ℱ , ( ℱ t ), ℙ ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to ℱ ∞ (the-algebra generated by ( ℱ t )) a coherent family of probability measures ( ℚ t ) indexed by , each of them being defined on ℱ t . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative...

Scaling laws for non-Euclidean plates and the isometric immersions of Riemannian metrics

Marta Lewicka, Mohammad Reza Pakzad (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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Recall that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one seeks a deformation yielding the closest metric realization. We set up a variational formulation of this problem by introducing the non-Euclidean version of the nonlinear elasticity functional, and establish its -convergence under...