The It\^{o} integral with respect to an infinite dimensional L\'{e}vy process: A series approach
Probability
2025-11-21 v1 Functional Analysis
Abstract
We present an alternative construction of the infinite dimensional It\^{o} integral with respect to a Hilbert space valued L\'{e}vy process. This approach is based on the well-known theory of real-valued stochastic integration, and the respective It\^{o} integral is given by a series of It\^{o} integrals with respect to standard L\'{e}vy processes. We also prove that this stochastic integral coincides with the It\^{o} integral that has been developed in the literature.
Keywords
Cite
@article{arxiv.1907.01450,
title = {The It\^{o} integral with respect to an infinite dimensional L\'{e}vy process: A series approach},
author = {Stefan Tappe},
journal= {arXiv preprint arXiv:1907.01450},
year = {2025}
}
Comments
21 pages