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With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust t...
Pier Giorgio Frassati is situated in the social and political upheaval of early-twentieth-century Italy. The Roman Catholic Church read the warning signs of atheistic Marxism; Mussolini filled Italy's political vacuum with fascists; and Rome was still Italy's disputed capital. The biography draws from a synopsis of selected letters and witness accounts, revealing Pier Giorgio's increasing engagement with the world around him, shaped by his spiritual life. Pier Giorgio belonged to an upper-middle-class family and his parents transmitted fundamental values of truth, courage, and justice. Although he was deeply loved by his parents, they did not share his religious zeal. Pier Giorgio was concer...