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On the uniform ergodic theorem in Banach spaces that do not contain duals

Vladimir Fonf, Michael Lin, Alexander Rubinov (1996)

Studia Mathematica

Let T be a power-bounded linear operator in a real Banach space X. We study the equality (*) ( I - T ) X = z X : s u p n k = 0 n T k z < . For X separable, we show that if T satisfies and is not uniformly ergodic, then ( I - T ) X ¯ contains an isomorphic copy of an infinite-dimensional dual Banach space. Consequently, if X is separable and does not contain isomorphic copies of infinite-dimensional dual Banach spaces, then (*) is equivalent to uniform ergodicity. As an application, sufficient conditions for uniform ergodicity of irreducible Markov chains...

On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions

Freddy Delbaen, Ying Hu, Adrien Richou (2011)

Annales de l'I.H.P. Probabilités et statistiques

In [Probab. Theory Related Fields141 (2008) 543–567], the authors proved the uniqueness among the solutions of quadratic BSDEs with convex generators and unbounded terminal conditions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman–Kac formula proved...

On the volume of intersection of three independent Wiener sausages

M. van den Berg (2010)

Annales de l'I.H.P. Probabilités et statistiques

Let K be a compact, non-polar set in ℝm, m≥3 and let SKi(t)={Bi(s)+y: 0≤s≤t, y∈K} be Wiener sausages associated to independent brownian motions Bi, i=1, 2, 3 starting at 0. The expectation of volume of ⋂i=13SKi(t) with respect to product measure is obtained in terms of the equilibrium measure of K in the limit of large t.

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