On the Signature of a Path in an Operator Algebra

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2022
• Автори: Gilliers, Nicolas, Bellingeri, Carlo
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2022
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/211808
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: On the Signature of a Path in an Operator Algebra. Nicolas Gilliers and Carlo Bellingeri. SIGMA 18 (2022), 096, 43 pages

We introduce a class of operators associated with the signature of a smooth path 𝑋 with values in a 𝐶⋆ algebra 𝒜. These operators serve as the basis of Taylor expansions of solutions to controlled differential equations of interest in noncommutative probability. They are defined by fully contracting...