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From Levy-Type Processes to Parabolic SPDEs (Paperback, 1st ed. 2016)
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From Levy-Type Processes to Parabolic SPDEs (Paperback, 1st ed. 2016)
Series: Advanced Courses in Mathematics - CRM Barcelona
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Total price: R1,806
Discovery Miles: 18 060
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This volume presents the lecture notes from two courses given by
Davar Khoshnevisan and Rene Schilling, respectively, at the second
Barcelona Summer School on Stochastic Analysis. Rene Schilling's
notes are an expanded version of his course on Levy and Levy-type
processes, the purpose of which is two-fold: on the one hand, the
course presents in detail selected properties of the Levy
processes, mainly as Markov processes, and their different
constructions, eventually leading to the celebrated Levy-Ito
decomposition. On the other, it identifies the infinitesimal
generator of the Levy process as a pseudo-differential operator
whose symbol is the characteristic exponent of the process, making
it possible to study the properties of Feller processes as space
inhomogeneous processes that locally behave like Levy processes.
The presentation is self-contained, and includes dedicated chapters
that review Markov processes, operator semigroups, random measures,
etc. In turn, Davar Khoshnevisan's course investigates selected
problems in the field of stochastic partial differential equations
of parabolic type. More precisely, the main objective is to
establish an Invariance Principle for those equations in a rather
general setting, and to deduce, as an application, comparison-type
results. The framework in which these problems are addressed goes
beyond the classical setting, in the sense that the driving noise
is assumed to be a multiplicative space-time white noise on a
group, and the underlying elliptic operator corresponds to a
generator of a Levy process on that group. This implies that
stochastic integration with respect to the above noise, as well as
the existence and uniqueness of a solution for the corresponding
equation, become relevant in their own right. These aspects are
also developed and supplemented by a wealth of illustrative
examples.
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