Stochastic Analysis of Mixed Fractional Gaussian Processes presents the main tools necessary to characterize Gaussian processes. The book focuses on the particular case of the linear combination of independent fractional and sub-fractional Brownian motions with different Hurst indices. Stochastic integration with respect to these processes is considered, as is the study of the existence and uniqueness of solutions of related SDE's. Applications in finance and statistics are also explored, with each chapter supplying a number of exercises to illustrate key concepts. - Presents both mixed fractional and sub-fractional Brownian motions - Provides an accessible description for mixed fractional gaussian processes that is ideal for Master's and PhD students - Includes different Hurst indices
Through application of the Smoothed Particle Hydrodynamics (SPH) method, this monograph mainly focuses on large deformations and flow failure simulations of geomaterials and movement behavior, which are always involved in geo-disasters. The work covers the theoretical background, numerical techniques, code implementation issues, and many novel and interesting applications. Two-dimensional and three-dimensional SPH models in the framework of both hydrodynamics and solid mechanics are established, with detailed descriptions. The monograph also contains many appealing and practical examples of geo-disaster modeling and analysis, including the fluidized movement of flow-like landslides, lateral spread of liquefied soils, and flow slides in landfills. In the documented SPH simulations, the propagation of geo-disasters is effectively reproduced. Dynamic behaviors of geomaterials during propagation are ascertained, including sliding path, flow velocity, maximum distance reached, and distribution of deposits. In this way, the monograph presents a means for mapping hazardous areas, estimating hazard intensity, and identifying and designing appropriate protective measures.
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