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Pathwise asymptotics for Volterra processes conditioned to a noisy version of the Brownian motion. (English) Zbl 1434.60093

Summary: In this paper we investigate a problem of large deviations for continuous Volterra processes under the influence of model disturbances. More precisely, we study the behavior, in the near future after \(T\), of a Volterra process driven by a Brownian motion in a case where the Brownian motion is not directly observable, but only a noisy version is observed or some linear functionals of the noisy version are observed. Some examples are discussed in both cases.

MSC:

60F10 Large deviations
60G15 Gaussian processes
60G22 Fractional processes, including fractional Brownian motion
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