Stochastic models, information theory, and lie groups v. I Classical results and geometric methods

A wide variety of problems in engineering and applied science can be formulated as diffusion processes on motion groups. Often, underlying phenomena associated with diffusion processes on motion groups have been rediscovered in the context of each new application area studied, and ad-hoc solution techniques have been derived each time. This textbook takes the unique perspective of presenting underlying equations that are the same in a variety of fields to developan elegant solution technique based on concepts from noncommutative harmonic analysis. Featuring extensive exercises and applications to optical communication systems, semi-flexible polymers, robotic manipulators, steerable needles, and bacterial chemotaxis, Stochastic Models and Lie Groups will be of interestto graduate students and researchers working in applied mathematics, the sciences, and engineering. Unique perspective: author presents underlying equations that are the same in a variety of fields to develop an elegant solution technique Concrete presentation makes it easy for readers to obtain numerical solutions for their own problems Extensive exercises Suitable as a textbook for advanced undergraduate and graduate courses in continuous-time stochastic processes or elementary differential geometry INDICE: Preface.- Introduction.- Gaussian Distributions and the Heat Equation.- Probability and Information Theory.- Stochastic Differential Equations.-Geometry of Curves and Surfaces.- Differential Forms.- Polytopes and Manifolds.- Stochastic Processes on Manifolds.- Summary.- Appendix. Review of Linear Algebra, Vector Calculus, and Systems Theory.- Index.

• ISBN: 978-0-8176-4802-2
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 410
• Fecha Publicación: 01/08/2009
• Nº Volúmenes: 1
• Idioma: Inglés