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A TUTORIAL INTRODUCTION TO STOCHASTIC …

A TUTORIAL INTRODUCTION TO STOCHASTICANALYSIS AND ITS APPLICATIONSbyIOANNIS KARATZASD epartment of StatisticsColumbia UniversityNew York, 10027 September 1988 SynopsisWe present in these lectures, in an informal manner, the very basic ideas and results ofstochastic calculus, including its chain rule, the fundamental theorems on the represen-tation of martingales as STOCHASTIC integrals and on the equivalent change of probabilitymeasure, as well as elements of STOCHASTIC differential equations. These results suffice fora rigorous treatment of important applications, such as filtering theory, STOCHASTIC con-trol, and the modern theory of financial economics.

Some familiarity with probability theory and stochastic processes, including a good understanding of conditional distributions and expectations, will be assumed.

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