Work

Generalized Euler–Maclaurin Formula and Signatures

Year: 2025

Type: article

Abstract: The Euler–Maclaurin formula, which relates a discrete sum with an integral, is generalised to the setting of Riemann–Stieltjes sums and integrals on stochastic processes whose paths are a.s. rectifiable, namely, continuous and with bounded variation. For this purpose, new variants of the signature are introduced, such as the flip and the sawtooth signature. The counterparts of the Bernoulli numbers that arise in the classical Euler–Maclaurin formula are shown to be the integration constants in the repeated integration by parts, which “recursively minimise the error” at every truncation level.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf092

Authors: Carlo Bellingeri, Peter K Friz, Sylvie Paycha

Institutions: Institut Élie Cartan de Lorraine, Université de Lorraine, Weierstrass Institute for Applied Analysis and Stochastics, Technische Universität Berlin, University of Potsdam

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W4409407210

FWCI:

Cites: 20

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Related to: 10