Dirichlet Forms Methods for Poisson Point Measures and Lévy by Nicolas Bouleau,Laurent Denis

By Nicolas Bouleau,Laurent Denis

A simplified method of Malliavin calculus tailored to Poisson random measures is built and utilized during this publication. known as the “lent particle technique” it really is in keeping with perturbation of the placement of debris. Poisson random measures describe phenomena regarding random jumps (for example in mathematical finance) or the random distribution of debris (as in statistical physics). because of the speculation of Dirichlet types, the authors advance a mathematical instrument for a rather basic type of random Poisson measures and considerably simplify computations of Malliavin matrices of Poisson functionals. the tactic supplies upward thrust to a brand new specific calculus that they illustrate on quite a few examples: it is composed in including a particle after which removal it after computing the gradient. utilizing this technique, possible determine absolute continuity of Poisson functionals equivalent to Lévy components, options of SDEs pushed by way of Poisson degree and, by way of generation, receive regularity of legislation. The authors additionally provide purposes to errors calculus theory.
This booklet could be of curiosity to researchers and graduate scholars within the fields of stochastic research and finance, and within the area of statistical physics. Professors getting ready classes on those subject matters also will locate it necessary. The prerequisite is a data of likelihood theory.

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