A simplified approach to Malliavin calculus adapted to Poisson
random measures is developed and applied in this book. Called the
"lent particle method" it is based on perturbation of the position
of particles. Poisson random measures describe phenomena involving
random jumps (for instance in mathematical finance) or the random
distribution of particles (as in statistical physics). Thanks to
the theory of Dirichlet forms, the authors develop a mathematical
tool for a quite general class of random Poisson measures and
significantly simplify computations of Malliavin matrices of
Poisson functionals. The method gives rise to a new explicit
calculus that they illustrate on various examples: it consists in
adding a particle and then removing it after computing the
gradient. Using this method, one can establish absolute continuity
of Poisson functionals such as Levy areas, solutions of SDEs driven
by Poisson measure and, by iteration, obtain regularity of laws.
The authors also give applications to error calculus theory. This
book will be of interest to researchers and graduate students in
the fields of stochastic analysis and finance, and in the domain of
statistical physics. Professors preparing courses on these topics
will also find it useful. The prerequisite is a knowledge of
probability theory.
General
| Imprint: |
Springer International Publishing AG
|
| Country of origin: |
Switzerland |
| Series: |
Probability Theory and Stochastic Modelling, 76 |
| Release date: |
March 2019 |
| First published: |
2015 |
| Authors: |
Nicolas Bouleau
• Laurent Denis
|
| Dimensions: |
235 x 155mm (L x W) |
| Format: |
Paperback
|
| Pages: |
323 |
| Edition: |
Softcover reprint of the original 1st ed. 2015 |
| ISBN-13: |
978-3-319-79845-5 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Probability & statistics
|
| LSN: |
3-319-79845-6 |
| Barcode: |
9783319798455 |
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