The Itô Integral with respect to an Infinite Dimensional Lévy Process : A Series Approach

Abstract EN

We present an alternative construction of the infinite dimensional Itô integral with respect to a Hilbert space valued Lévy process.

This approach is based on the well-known theory of real-valued stochastic integration, and the respective Itô integral is given by a series of Itô integrals with respect to standard Lévy processes.

We also prove that this stochastic integral coincides with the Itô integral that has been developed in the literature.