Stochastic Integration with respect to Volterra processes

Details Stochastic Integration with respect to Volterra processes Stochastic Integration with respect to Volterra processes

2003-02-05

arxiv.org/abs/math/0302047v1

Mathematics

Probability

Scientific paper

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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