A multiple stochastic integral with respect to a strictly p-stable random measure
The authors give a construction of a k-tuple stochastic integral (k\(\geq 2)\) relative to a strictly p-stable random measure for \(0<p\leq 2\). The integrands are deterministic functions with values in a Banach space E. The paper extends essentially the known results on multiple stochastic integrals relative to independently scattered random measures. The method of construction uses inequalities for random (p-stable) multilinear forms. The main idea is to use recently discovered so-called decoupling inequalities. These inequalities allow the reduction of certain basic problems of multiple stochastic integration to the study of series in independent random variables, and make it possible to reduce the non- symmetric case to the symmetric case. The richness of the space of E- valued functions for which the multiple stochastic integral exists is connected with geometric properties of the Banach space E, as e.g. E being of stable type p or E satisfying the so-called multilinear contraction principle.
scientific article; zbMATH DE number 4058561