Introductory Lectures on Fluctuations of Lévy Processes with Applications (eBook, PDF)
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Lévy processes are the natural continuous-time analogue of random walks; they form a rich class of stochastic processes around which a robust mathematical theory exists. Their mathematical significance is evident in their application in many areas of classical and modern stochastic models, including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance and continuous-state branching processes. This book aims to be mathematically rigourous while still providing an intuitive feel for underlying principles. The results and applications often fo...
Lévy processes are the natural continuous-time analogue of random walks; they form a rich class of stochastic processes around which a robust mathematical theory exists. Their mathematical significance is evident in their application in many areas of classical and modern stochastic models, including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance and continuous-state branching processes. This book aims to be mathematically rigourous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness. Each chapter includes a comprehensive set of exercises with complete solutions.
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