For which functions are 𝑓(𝑋_{𝑡})-𝔼𝕗(𝕏_{𝕥}) and 𝕘(𝕏_{𝕥})/𝔼𝕘(𝕏_{𝕥}) martingales?

DOI10.1090/tpms/1157zbMath1490.60100arXiv2107.11974OpenAlexW4226302895MaRDI QIDQ5018758

Franziska Kühn, Rene L. Schilling

Publication date: 22 December 2021

Published in: Theory of Probability and Mathematical Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.11974

zbMATH Keywords

harmonic polynomialBrownian motionmartingaleLévy processconvolution equationCauchy functional equationChoquet-Deny theorempolynomial process

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Brownian motion (60J65) Functional equations for real functions (39B22) Martingales with continuous parameter (60G44) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

Related Items (2)

The Butzer-Kozakiewicz article on Riemann derivatives of 1954 and its influence ⋮ Martingale transformations of Brownian motion with application to functional equations

Cites Work

• From Lévy-type processes to parabolic SPDEs. Edited by Lluís Quer-Sardanyons and Frederic Utzet
• A Liouville theorem for Lévy generators
• On martingale transformations of multidimensional Brownian motion
• Change of variable formulas for non-anticipative functionals
• A note on the existence of transition probability densities of Lévy processes
• Zeroes of Infinitely Divisible Densities
• On the Riemann Derivatives for Integrable Functions
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