FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W49280145> ?p ?o ?g. }

• W49280145 abstract "This doctoral thesis lies within the framework of stochastic differential geometry and is structured in four chapters, Its goal is conveying to the geometric mechanics community the wealth of global tools available to handle mechanical problems that contain a stochastic component and that do not seem to have been exploited to the full extent of their potential. After an introductory chapter aimed at recalling the main basics of stochastic calculus both in Euclidean spaces and manifolds, the new contributions of the thesis are contained in the subsequent chapters. In Chapter 2, we use the global stochastic analysis tools introduced by P. A. Meyer and L. Schwartz to write down a stochastic generalization of the Hamilton equations on a Poisson manifold that, for exact symplectic manifolds, are characterized by a natural critical action principle similar to the one encountered in classical mechanics. Several features and examples in relation with the solution semimartingales of these equations are presented. We extend then some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical situation, it is written as a function of the configuration space using a regular Lagrangian submanifold. Additionally, we will use a variation of the Hamilton-Jacobi equation to characterize the generating functions of one-parameter groups of symplectomorphisms that allow one to rewrite a given stochastic Hamiltonian system in a form whose solutions are very easy to find; this result recovers in the stochastic context the classical solution method by reduction to the equilibrium of a Hamiltonian system. In Chapter 3, we present reduction and reconstruction procedures for the solutions of symmetric stochastic differential equations, similar to those available for ordinary differential equations. Additionally, we use the local tangent-normal decomposition, available when the symmetry group is proper, to construct local skew-product splittings in a neighborhood of any point in the open and dense principal orbit type. The general methods introduced are then adapted to the Hamiltonian case, which is studied with special care and illustrated with several examples. The Hamiltonian category deserves a separate study since in that situation the presence of symmetries implies in most cases the existence of conservation laws, mathematically described via momentum maps, that should be taken into account in the analysis. Finally, Chapter 4 proves a version for stochastic differential equations of the Lie-Scheffers Theorem. This result characterizes the existence of nonlinear superposition rules for the general solution of those equations in terms of the involution properties of the distribution generated by the vector fields that define it. When stated in the particular case of standard deterministic systems, our main theorem improves various aspects of the classical Lie-Scheffers result. We show that the stochastic analog of the classical Lie-Scheffers systems can be reduced to the study of Lie group valued stochastic Lie-Scheffers systems; those systems, as well as those taking values in homogeneous spaces are studied in detail. These developments are illustrated with several examples." @default.
• W49280145 created "2016-06-24" @default.
• W49280145 creator A5007288437 @default.
• W49280145 date "2008-01-01" @default.
• W49280145 modified "2023-09-24" @default.
• W49280145 title "Stochastic geometric mechanics" @default.
• W49280145 hasPublicationYear "2008" @default.
• W49280145 type Work @default.
• W49280145 sameAs 49280145 @default.
• W49280145 citedByCount "2" @default.
• W49280145 countsByYear W492801452013 @default.
• W49280145 crossrefType "journal-article" @default.
• W49280145 hasAuthorship W49280145A5007288437 @default.
• W49280145 hasConcept C105795698 @default.
• W49280145 hasConcept C109798219 @default.
• W49280145 hasConcept C11255438 @default.
• W49280145 hasConcept C121332964 @default.
• W49280145 hasConcept C121770821 @default.
• W49280145 hasConcept C134306372 @default.
• W49280145 hasConcept C136864674 @default.
• W49280145 hasConcept C143218062 @default.
• W49280145 hasConcept C151342819 @default.
• W49280145 hasConcept C15184713 @default.
• W49280145 hasConcept C157434478 @default.
• W49280145 hasConcept C16672771 @default.
• W49280145 hasConcept C168619227 @default.
• W49280145 hasConcept C177715462 @default.
• W49280145 hasConcept C186450821 @default.
• W49280145 hasConcept C2778860007 @default.
• W49280145 hasConcept C2780791683 @default.
• W49280145 hasConcept C28826006 @default.
• W49280145 hasConcept C33923547 @default.
• W49280145 hasConcept C51955184 @default.
• W49280145 hasConcept C62520636 @default.
• W49280145 hasConcept C63331456 @default.
• W49280145 hasConcept C74650414 @default.
• W49280145 hasConcept C8272713 @default.
• W49280145 hasConcept C84114770 @default.
• W49280145 hasConcept C84629840 @default.
• W49280145 hasConcept C93779851 @default.
• W49280145 hasConcept C97355855 @default.
• W49280145 hasConceptScore W49280145C105795698 @default.
• W49280145 hasConceptScore W49280145C109798219 @default.
• W49280145 hasConceptScore W49280145C11255438 @default.
• W49280145 hasConceptScore W49280145C121332964 @default.
• W49280145 hasConceptScore W49280145C121770821 @default.
• W49280145 hasConceptScore W49280145C134306372 @default.
• W49280145 hasConceptScore W49280145C136864674 @default.
• W49280145 hasConceptScore W49280145C143218062 @default.
• W49280145 hasConceptScore W49280145C151342819 @default.
• W49280145 hasConceptScore W49280145C15184713 @default.
• W49280145 hasConceptScore W49280145C157434478 @default.
• W49280145 hasConceptScore W49280145C16672771 @default.
• W49280145 hasConceptScore W49280145C168619227 @default.
• W49280145 hasConceptScore W49280145C177715462 @default.
• W49280145 hasConceptScore W49280145C186450821 @default.
• W49280145 hasConceptScore W49280145C2778860007 @default.
• W49280145 hasConceptScore W49280145C2780791683 @default.
• W49280145 hasConceptScore W49280145C28826006 @default.
• W49280145 hasConceptScore W49280145C33923547 @default.
• W49280145 hasConceptScore W49280145C51955184 @default.
• W49280145 hasConceptScore W49280145C62520636 @default.
• W49280145 hasConceptScore W49280145C63331456 @default.
• W49280145 hasConceptScore W49280145C74650414 @default.
• W49280145 hasConceptScore W49280145C8272713 @default.
• W49280145 hasConceptScore W49280145C84114770 @default.
• W49280145 hasConceptScore W49280145C84629840 @default.
• W49280145 hasConceptScore W49280145C93779851 @default.
• W49280145 hasConceptScore W49280145C97355855 @default.
• W49280145 hasLocation W492801451 @default.
• W49280145 hasOpenAccess W49280145 @default.
• W49280145 hasPrimaryLocation W492801451 @default.
• W49280145 hasRelatedWork W1043690781 @default.
• W49280145 hasRelatedWork W1452281256 @default.
• W49280145 hasRelatedWork W188634349 @default.
• W49280145 hasRelatedWork W1993964363 @default.
• W49280145 hasRelatedWork W1999717221 @default.
• W49280145 hasRelatedWork W2004868751 @default.
• W49280145 hasRelatedWork W2019458053 @default.
• W49280145 hasRelatedWork W2019621538 @default.
• W49280145 hasRelatedWork W2070183849 @default.
• W49280145 hasRelatedWork W2089759842 @default.
• W49280145 hasRelatedWork W2246676560 @default.
• W49280145 hasRelatedWork W2771500741 @default.
• W49280145 hasRelatedWork W2790059262 @default.
• W49280145 hasRelatedWork W2962897903 @default.
• W49280145 hasRelatedWork W2966609299 @default.
• W49280145 hasRelatedWork W2978819269 @default.
• W49280145 hasRelatedWork W3107842889 @default.
• W49280145 hasRelatedWork W3128256072 @default.
• W49280145 hasRelatedWork W332955864 @default.
• W49280145 hasRelatedWork W84963904 @default.
• W49280145 isParatext "false" @default.
• W49280145 isRetracted "false" @default.
• W49280145 magId "49280145" @default.
• W49280145 workType "article" @default.