First Course in Stochastic Calculus

Louis-Pierre Arguin, Baruch College, City University of New York, NY, and Graduate Center, City University of New York, NY.

• Basic notions of probabilityGaussian processesProperties of Brownian motionMartingalesIto calculusMultivariate Ito calculusIto processes and stochastic differential equationsThe Markov propertyChange of probabilityApplications to mathematical financeBibliographyIndex

Louis-Pierre Arguin's masterly introduction to stochastic calculus seduces the reader with its quietly conversational style; even rigorous proofs seem natural and easy. Full of insights and intuition, reinforced with many examples, numerical projects, and exercises, this book by a prize-winning mathematician and great teacher fully lives up to the author's reputation. I give it my strongest possible recommendation."" —Jim Gatheral, Baruch College""I happen to be of a different persuasion, about how stochastic processes should be taught to undergraduate and MA students. But I have long been thinking to go against my own grain at some point and try to teach the subject at this level—together with its applications to finance—in one semester. Louis-Pierre Arguin's excellent and artfully designed text will give me the ideal vehicle to do so."" —Ioannis Karatzas, Columbia University, New York