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Stochastic Partial Differential Equations: An Introduction (Paperback, 1st ed. 2015)
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Stochastic Partial Differential Equations: An Introduction (Paperback, 1st ed. 2015)
Series: Universitext
Expected to ship within 12 - 17 working days
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This book provides an introduction to the theory of stochastic
partial differential equations (SPDEs) of evolutionary type. SPDEs
are one of the main research directions in probability theory with
several wide ranging applications. Many types of dynamics with
stochastic influence in nature or man-made complex systems can be
modelled by such equations. The theory of SPDEs is based both on
the theory of deterministic partial differential equations, as well
as on modern stochastic analysis. Whilst this volume mainly follows
the 'variational approach', it also contains a short account on the
'semigroup (or mild solution) approach'. In particular, the volume
contains a complete presentation of the main existence and
uniqueness results in the case of locally monotone coefficients.
Various types of generalized coercivity conditions are shown to
guarantee non-explosion, but also a systematic approach to treat
SPDEs with explosion in finite time is developed. It is, so far,
the only book where the latter and the 'locally monotone case' is
presented in a detailed and complete way for SPDEs. The extension
to this more general framework for SPDEs, for example, in
comparison to the well-known case of globally monotone
coefficients, substantially widens the applicability of the
results.
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