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A note on stochastic integrals as $L^2$-curves

Probability 2025-11-21 v1

Abstract

In a work of van Gaans (2005a) stochastic integrals are regarded as L2L^2-curves. In Filipovi\'{c} and Tappe (2008) we have shown the connection to the usual It\^o-integral for c\`adl\`ag-integrands. The goal of this note is to complete this result and to provide the full connection to the It\^o-integral. We also sketch an application to stochastic partial differential equations.

Keywords

Cite

@article{arxiv.1907.03258,
  title  = {A note on stochastic integrals as $L^2$-curves},
  author = {Stefan Tappe},
  journal= {arXiv preprint arXiv:1907.03258},
  year   = {2025}
}

Comments

6 pages

R2 v1 2026-06-23T10:14:06.336Z