Abstract
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.
Highlights
In this paper we study the asymptotics of the regular conditional prediction law of a Gaussian Volterra process in a case where one does not observe the process directly, but instead observes a noisy version of it
Given the σ -algebra FTα,α, where (Ftα,α )t≥0 is the filtration generated by the mixed Brownian motion W α,α, i.e. we want to condition the process to the past of the mixed
Suppose ((Utε)t∈[0,1])ε>0 is a family of centered Gaussian processes, defined on the probability space (, F, P), that satisfies a large deviation principle on C[0, 1] with the inverse speed ηε and the good rate function I
Summary
In this paper we study the asymptotics of the regular conditional prediction law of a Gaussian Volterra process in a case where one does not observe the process directly, but instead observes a noisy version of it.
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