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Introduction to Stochastic Calculus

Introduction to Stochastic CalculusMath 545 - Duke UniversityAndrea Agazzi, Jonathan C. MattinglyContentsChapter 1. Introduction51. Motivations52. Outline For a Course6 Chapter 2. Probabilistic Background91. Countable probability spaces92. Uncountable Probability Spaces123. General Probability Spaces and Sigma Algebras134. Distributions and Convergence of Random Variables20 Chapter 3. Brownian Motion and Stochastic Processes231. An Illustrative Example: A Collection of Random Walks232. General Stochastic Proceses243. Definition of Brownian motion (Wiener Process)254. Constructive Approach to Brownian motion285. Brownian motion has Rough Trajectories296.

model the number of genetic mutations an animal species. We may also think about Nptqas the number of sick individuals in a population. Reasonable and widely applied models for the spread of infectious diseases are obtained by modifying (1.1), and observing its behavior. In all these cases, one may be interested in knowing if it is likely for the

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