Stochastic Calculus in Infinite Dimensions and SPDEs - 9783031695858

Stochastic Calculus in Infinite Dimensions and SPDEsAuthor(s): Daniel Goodair, Dan Crisan\nFormat: Paperback\nPublisher: Springer International Publishing AG, Switzerland\nImprint: Springer International Publishing AG\nISBN-13: 9783031695858, 978-3031695858\nSynopsis\nIntroducing a groundbreaking framework for stochastic partial differential equations (SPDEs), this work presents three significant advancements over the traditional variational approach.\n\nFirstly, Stratonovich SPDEs are explicitly addressed. Widely used in physics, Stratonovich SPDEs have typically been converted to Ito form for mathematical treatment. While this conversion is understood heuristically, a comprehensive treatment in infinite dimensions has been lacking, primarily due to insufficient rigorous results on martingale properties.\n\nSecondly, the framework incorporates differential noise, assuming the noise operator is only bounded from a smaller Hilbert space into a larger one, rather than within the same s.