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Are there any good, rigorous and preferably modern books or papers on path integral approach to Gaussian processes? I am interested in both introductory level and deeper monographs on the subject.

I would very much like the reference to at least include the fractional Brownian motion process treated in terms of its action functional and maybe some information on the relation to the standard definitions/representations of fBm.

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  • $\begingroup$ I suppose one can think of the Malliavin calculus and Rough-paths built for fBM as a path integral approach i.e. study of functionals built out of fBM/Gaussian processes. "Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion" and "A construction of the rough path above fractional Brownian...". In fact, regularity structures was used in studying more general path-integrals measures in "Geometric stochastic heat equations". $\endgroup$
    – Thomas Kojar
    Commented Jun 18, 2022 at 17:59

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I know only of a single book on path integrals that includes the case of fractional Brownian motion:

Path Integrals for Stochastic Processes: An Introduction by Horacio S. Wio.

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