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Introductory Lectures on Fluctuations of LA©vy Processes with Applications (Universitext)

Introductory Lectures on Fluctuations of LA©vy Processes with Applications (Universitext)

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Описание
LA©vy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their mathematical significance is justified by their application in many areas of classical and modern stochastic models. This textbook forms the basis of a graduate course on the theory and applications of LA©vy processes, from the perspective of their path fluctuations. Central to the presentation are decompositions of the paths of LA©vy processes in terms of their local maxima and an understanding of their short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of LA©vy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness. Each chapter has a comprehensive set of exercises with complete solutions.