The purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical Levy-Khinchin representation. It interweaves probability theory, topology, and global analysis on manifolds to present the most recent results in a developing area of stochastic analysis. The author's discussion is structured with three different levels of generality:- A Markov process in a Lie group G that is invariant under the left (or right) translations- A Markov process xt in a manifold X that is invariant under the transitive action of a Lie group G on X- A Markov process xt invariant under the non-transitive action of a Lie group GA large portion of the text is devoted to the representation of inhomogeneous Levy processes in Lie groups and homogeneous spaces by a time dependent triple through a martingale property. Preliminary definitions and results in both stochastics and Lie groups are provided in a series of appendices, making the book accessible to those who may be non-specialists in either of these areas. Invariant Markov Processes Under Lie Group Actions will be of interest to researchers in stochastic analysis and probability theory, and will also appeal to experts in Lie groups, differential geometry, and related topics interested in applications of their own subjects.

The theory of Levy processes in Lie groups is not merely an extension of the theory of Levy processes in Euclidean spaces. Because of the unique structures possessed by non-commutative Lie groups, these processes exhibit certain interesting limiting properties which are not present for their counterparts in Euclidean spaces. These properties reveal a deep connection between the behaviour of the stochastic processes and the underlying algebraic and geometric structures of the Lie groups themselves. The purpose of this work is to provide an introduction to Levy processes in general Lie groups, the limiting properties of Levy processes in semi-simple Lie groups of non-compact type and the dynamical behavior of such processes as stochastic flows on certain homogeneous spaces. The reader is assumed to be familiar with Lie groups and stochastic analysis, but no prior knowledge of semi-simple Lie groups is required.

Many Smart Grid books include "privacy" in their title, but only touch on privacy, with most of the discussion focusing on cybersecurity. Filling this knowledge gap, Data Privacy for the Smart Grid provides a clear description of the Smart Grid ecosystem, presents practical guidance about its privacy risks, and details the actions required to protect data generated by Smart Grid technologies. It addresses privacy in electric, natural gas, and water grids and supplies two different perspectives of the topic-one from a Smart Grid expert and another from a privacy and information security expert.The authors have extensive experience with utilities and leading the U.S. government's National Institute of Standards and Technologies (NIST) Cyber Security Working Group (CSWG)/Smart Grid Interoperability Group (SGIP) Privacy Subgroup. This comprehensive book is understandable for all those involved in the Smart Grid. The authors detail the facts about Smart Grid privacy so readers can separate truth from myth about Smart Grid privacy. While considering privacy in the Smart Grid, the book also examines the data created by Smart Grid technologies and machine-to-machine (M2M) applications and associated legal issues.The text details guidelines based on the Organization for Economic Cooperation and Development Privacy Guidelines and the U.S. Federal Trade Commission Fair Information Practices. It includes privacy training recommendations and references to additional Smart Grid privacy resources. After reading the book, readers will be prepared to develop informed opinions, establish fact-based decisions, make meaningful contributions to Smart Grid legislation and policies, and to build technologies to preserve and protect privacy. Policy makers; Smart Grid and M2M product and service developers; utility customer and privacy resources; and other service providers and resources are primary beneficiaries of the information provided in

Many Smart Grid books include "privacy" in their title, but only touch on privacy, with most of the discussion focusing on cybersecurity. Filling this knowledge gap, Data Privacy for the Smart Grid provides a clear description of the Smart Grid ecosystem, presents practical guidance about its privacy risks, and details the actions required to protect data generated by Smart Grid technologies. It addresses privacy in electric, natural gas, and water grids and supplies two different perspectives of the topic-one from a Smart Grid expert and another from a privacy and information security expert.The authors have extensive experience with utilities and leading the U.S. government's National Institute of Standards and Technologies (NIST) Cyber Security Working Group (CSWG)/Smart Grid Interoperability Group (SGIP) Privacy Subgroup. This comprehensive book is understandable for all those involved in the Smart Grid. The authors detail the facts about Smart Grid privacy so readers can separate truth from myth about Smart Grid privacy. While considering privacy in the Smart Grid, the book also examines the data created by Smart Grid technologies and machine-to-machine (M2M) applications and associated legal issues.The text details guidelines based on the Organization for Economic Cooperation and Development Privacy Guidelines and the U.S. Federal Trade Commission Fair Information Practices. It includes privacy training recommendations and references to additional Smart Grid privacy resources. After reading the book, readers will be prepared to develop informed opinions, establish fact-based decisions, make meaningful contributions to Smart Grid legislation and policies, and to build technologies to preserve and protect privacy. Policy makers; Smart Grid and M2M product and service developers; utility customer and privacy resources; and other service providers and resources are primary beneficiaries of the information provided in