The stochastic partial differential equations (SPDEs) arise in many
applications of the probability theory. This monograph will focus
on two particular (and probably the most known) equations: the
stochastic heat equation and the stochastic wave equation.The focus
is on the relationship between the solutions to the SPDEs and the
fractional Brownian motion (and related processes). An important
point of the analysis is the study of the asymptotic behavior of
the p-variations of the solutions to the heat or wave equations
driven by space-time Gaussian noise or by a Gaussian noise with a
non-trivial correlation in space.The book is addressed to public
with a reasonable background in probability theory. The idea is to
keep it self-contained and avoid using of complex techniques. We
also chose to insist on the basic properties of the random noise
and to detail the construction of the Wiener integration with
respect to them. The intention is to present the proofs complete
and detailed.
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