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Rough Volterra equations. II: Convolutional generalized integrals. (English) Zbl 1223.60031
There are defined and solved Volterra equations driven by non-differentiable signals, by means of a variant of the rough paths theory which allows to handle generalized integrals weighted by an exponential coefficient. The results apply to the convolutional Volterra equations which include the case of the fractional Brownian motion with Hurst index \(>1/3\).
For Part I see [Stoch. Dyn. 9, No. 3, 437–477 (2009; Zbl 1181.60105)].

MSC:
60H05 Stochastic integrals
60H07 Stochastic calculus of variations and the Malliavin calculus
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