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Continuity of stochastic convolutions

Zdzisław Brzeźniak, Szymon Peszat, Jerzy Zabczyk (2001)

Czechoslovak Mathematical Journal

Let B be a Brownian motion, and let 𝒞 p be the space of all continuous periodic functions f with period 1. It is shown that the set of all f 𝒞 p such that the stochastic convolution X f , B ( t ) = 0 t f ( t - s ) d B ( s ) , t [ 0 , 1 ] does not have a modification with bounded trajectories, and consequently does not have a continuous modification, is of the second Baire category.

Convergence analysis for asymmetric Deffuant-Weisbuch model

Jiangbo Zhang (2014)

Kybernetika

In this paper, we investigate the convergence behavior of the asymmetric Deffuant-Weisbuch (DW) models during the opinion evolution. Based on the convergence of the asymmetric DW model that generalizes the conventional DW model, we first propose a new concept, the separation time, to study the transient behavior during the DW model's opinion evolution. Then we provide an upper bound of the expected separation time with the help of stochastic analysis. Finally, we show relations of the separation...

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