In Chapter 1, the author motivates the study of some of the abstract stochastic differential equations considered in this book by modeling real-life problems such as a heat equation, an electric circuit, an interacting particle system, a lumped control system, the stock price and option price dynamics.Chapter 2 introduces the necessary background from semigroup theory, particularly, the Yosida approximations and their properties, basics from analysis and probability in Banach spaces, stochastic calculus, the stochastic Fubini theorem, stochastic convolution integrals, Burkholder type inequalities, bounded stochastic integral contractors.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.