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Displaying similar documents to “Stochastic analysis of Bernoulli processes.”

A local convergence theorem for partial sums of stochastic adapted sequences

Wei Guo Yang, Zhong Xing Ye, Liu, Wen (2006)

Czechoslovak Mathematical Journal

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In this paper we establish a new local convergence theorem for partial sums of arbitrary stochastic adapted sequences. As corollaries, we generalize some recently obtained results and prove a limit theorem for the entropy density of an arbitrary information source, which is an extension of case of nonhomogeneous Markov chains.

Multilinear operators on C ( K , X ) spaces

Ignacio Villanueva (2004)

Czechoslovak Mathematical Journal

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Given Banach spaces  X , Y and a compact Hausdorff space  K , we use polymeasures to give necessary conditions for a multilinear operator from C ( K , X ) into  Y to be completely continuous (resp.  unconditionally converging). We deduce necessary and sufficient conditions for  X to have the Schur property (resp.  to contain no copy of  c 0 ), and for  K to be scattered. This extends results concerning linear operators.

On homeomorphic and diffeomorphic solutions of the Abel equation on the plane

Zbigniew Leśniak (1993)

Annales Polonici Mathematici

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We consider the Abel equation φ[f(x)] = φ(x) + a on the plane ℝ², where f is a free mapping (i.e. f is an orientation preserving homeomorphism of the plane onto itself with no fixed points). We find all its homeomorphic and diffeomorphic solutions φ having positive Jacobian. Moreover, we give some conditions which are equivalent to f being conjugate to a translation.