Stochastic Analysis Calculus

by Hiroyuki Matsumoto (Author), Setsuo Taniguchi (Author)

Network calculus, a theory dealing with queuing systems found in computer networks, focuses on performance guarantees. The development of an information theory for stochastic service-guarantee analysis has been identified as a grand challenge for future networking research. Towards that end, stochastic network calculus, the probabilistic version or generalization of the (deterministic) Network Calculus, has been recognized by researchers as a crucial step.

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis.

Introductory Stochastic Analysis for Finance and Insurance introduces readers to the topics needed to master and use basic stochastic analysis techniques for mathematical finance. The author presents the theories of stochastic processes and stochastic calculus and provides the necessary tools for modeling and pricing in finance and insurance. Practical in focus, the book's emphasis is on application, intuition, and computation, rather than theory.

The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the core mathematical discipline. Stochastic analysis provides a fruitful interpretation of this calculus, particularly as described by David Nualart and the scores of mathematicians he influences and with whom he collaborates.