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Representations of groups --- Mathematical physics. --- Hamiltonian systems --- Physical mathematics --- Physics --- Mathematics --- Representacions de grups --- Física matemàtica --- Sistemes hamiltonians --- Mecànica de Hamilton --- Mecànica hamiltoniana --- Sistemes de Hamilton --- Sistemes dinàmics de Hamilton --- Sistemes dinàmics diferenciables --- Equacions de Hamilton-Jacobi --- Mecànica --- Acústica --- Anàlisi de sistemes --- Anàlisi dimensional --- Grups quàntics --- Elasticitat --- Equació de Yang-Baxter --- Matemàtica en l'electrònica --- Problemes de contorn --- Teoria del potencial (Física) --- Teoria ergòdica --- Teories no lineals --- Rutes aleatòries (Matemàtica) --- Representació de grups (Matemàtica) --- Teoria de grups --- Fórmules de traça --- Grups simètrics --- Representacions de semigrups --- Representacions integrals
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This book provides an accessible overview concerning the stochastic numerical methods inheriting long-time dynamical behaviours of finite and infinite-dimensional stochastic Hamiltonian systems. The long-time dynamical behaviours under study involve symplectic structure, invariants, ergodicity and invariant measure. The emphasis is placed on the systematic construction and the probabilistic superiority of stochastic symplectic methods, which preserve the geometric structure of the stochastic flow of stochastic Hamiltonian systems. The problems considered in this book are related to several fascinating research hotspots: numerical analysis, stochastic analysis, ergodic theory, stochastic ordinary and partial differential equations, and rough path theory. This book will appeal to researchers who are interested in these topics.
Numerical analysis. --- Dynamical systems. --- Probabilities. --- Numerical Analysis. --- Dynamical Systems. --- Probability Theory. --- Sistemes hamiltonians --- Equacions diferencials estocàstiques --- Grups simplèctics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical analysis --- Grups algebraics lineals --- Anàlisi numèrica --- Equació de Fokker-Planck --- Mecànica de Hamilton --- Mecànica hamiltoniana --- Sistemes de Hamilton --- Sistemes dinàmics de Hamilton --- Sistemes dinàmics diferenciables --- Equacions de Hamilton-Jacobi --- Hamiltonian systems. --- Stochastic differential equations. --- Symplectic groups. --- Groups, Symplectic --- Linear algebraic groups --- Differential equations --- Fokker-Planck equation --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems
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