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I need some references about Volterra processes $Y=(Y_t)_{t\geq0}$ defined as $$ Y_t:=\int_{0}^{t} g(t,s)dB_s, \ \ t\geq 0,$$

where $B=\left(B_t\right)_{t\geq0}$ is a brownian motion and $g$ satisfies $\int_{0}^{t} g(t,s)^2ds<\infty$.

Even general references on the integration of deterministic functions wrt Brownian motion would be fine.

Thanks

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  • $\begingroup$ What exactly are you looking for? References about what kinds of properties? $\endgroup$
    – user479223
    Commented Jun 2, 2023 at 12:03
  • $\begingroup$ Basic theoretical fact. $\endgroup$
    – Joegin
    Commented Jun 2, 2023 at 12:54

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one source of many references about Voltera processes and a stochastic calculus for them is in

"Stochastic integration with respect to Volterra processes" by L. Decreusefond.

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