Stochastic Integration with respect to Volterra processes

2003/02/05 by L. Decreusefond, Decreusefond, L. · 1 citation
Mathematics · #60H07 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60H07

paper · pdf · doi:10.48550/arxiv.math/0302047

arxiv created 2003/02/05 · arxiv updated 2009/11/30

Abstract

We construct the basis of a stochastic calculus for so-called Volterra processes, i.e., processes which are defined as the stochastic integral of a time-dependent kernel with respect to a standard Brownian motion. For these processes which are natural generalization of fractional Brownian motion, we construct a stochastic integral and show some of its main properties: regularity with respect to time and kernel, transformation under an absolutely continuous change of probability, possible approximation schemes and Ito formula.

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