FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2028298308> ?p ?o ?g. }

• W2028298308 endingPage "181" @default.
• W2028298308 startingPage "119" @default.
• W2028298308 abstract "The theory of integration in infinite dimensions is in some sense the backbone of probability theory. On this backbone the stochastic calculus of variations has given rise to the flesh of differential calculus. Its first step is the construction at each point of the probability space of a Cameron–Martin-like tangent space in which the desired differential calculus can be developed. This construction proceeds along the lines of first-order differential geometry. In this paper we address the following questions: what could be the meaning of “curvature of the probability space”—how and why? How can curvatures be defined and computed? Why could a second-order differential geometry be relevant to stochastic analysis? We try to answer these questions for the probability space associated to the Brownian motion of a compact Riemannian manifold. Why? A basicenergy identity for anticipative stochastic integralswill be obtained as a byproduct of our computation of curvature. How? There are essentially four bottlenecks in the development of differential geometry on Wiener–Riemann manifolds: (i) the difficulty of finding an atlas of local charts such that the changes of charts preserve the class of the Wiener-like measures together with their associated Cameron–Martin-like tangent spaces; (ii) the difficulty of finding cylindrical approximations preserving the natural geometrical objects; (iii) the difficulty of renormalizing the divergent series to which the summation operations of finite dimensional differential geometry give rise in the non intrinsic context of local charts; (iv) the nonavailability of the computational procedures analogous to the local coordinates systems of the classical differential geometry. In the context of path space, the Itô filtration provides a much richer structure than that available in the framework of an abstract Wiener–Riemann manifold. Our work is a systematic attempt to replace the machinery of local charts with amethodology of moving frames. In our context, stochastic parallel transport provides a canonical moving frame on the path space. The concept of a cylindrical approximation has to be reshaped in our new situation into some geometric limit theorems, establishing that the Riemannian geometric objects of the cylindrical approximations induce by a limiting procedure geometric objects on the path space. Those limit theorems are reminiscent of the classical theorems which say that a Stratonovich SDE is the limit of an appropriate sequence of ODE. The canonical coordinate system provided by the moving frame will make it possible to proceed to the needed renormalizations byintrinsicstochastic integrals; in this context the anticipative stochastic integral theory of Nualart and Pardoux will play a decisive role. Finally, the moving frame will provide aneffective algorithm of computation for this differential geometry in infinite dimensions. In our study we encounter a new type of renormalization, thehypoelliptic renormalization, which corresponds to the fact that the bracket of smooth vector fields taking their values in the Cameron–Martin space can get out of this Cameron–Martin space. This hypoelliptic problem induces the nonrenormalizability of some geometrical objects. It leads also to a concept oftangent processesto probability spaces extending that based on the Cameron–Martin Theorem. For tangent processes a formula of integration by parts still holds; furthermore the tangent processes form a Lie algebra under the bracket. On the other hand, tangent processes cannot be stochastically integrated: this operation is well defined only for Cameron–Martin-type vector fields." @default.
• W2028298308 created "2016-06-24" @default.
• W2028298308 creator A5019439001 @default.
• W2028298308 creator A5072971888 @default.
• W2028298308 date "1996-07-01" @default.
• W2028298308 modified "2023-09-27" @default.
• W2028298308 title "Renormalized Differential Geometry on Path Space: Structural Equation, Curvature" @default.
• W2028298308 cites W1523213083 @default.
• W2028298308 cites W2031609484 @default.
• W2028298308 cites W2034632473 @default.
• W2028298308 cites W2052852643 @default.
• W2028298308 cites W2067555259 @default.
• W2028298308 cites W2079982785 @default.
• W2028298308 cites W2134182607 @default.
• W2028298308 cites W2525171208 @default.
• W2028298308 doi "https://doi.org/10.1006/jfan.1996.0081" @default.
• W2028298308 hasPublicationYear "1996" @default.
• W2028298308 type Work @default.
• W2028298308 sameAs 2028298308 @default.
• W2028298308 citedByCount "88" @default.
• W2028298308 countsByYear W20282983082013 @default.
• W2028298308 countsByYear W20282983082014 @default.
• W2028298308 countsByYear W20282983082015 @default.
• W2028298308 countsByYear W20282983082016 @default.
• W2028298308 countsByYear W20282983082017 @default.
• W2028298308 countsByYear W20282983082019 @default.
• W2028298308 countsByYear W20282983082021 @default.
• W2028298308 countsByYear W20282983082022 @default.
• W2028298308 crossrefType "journal-article" @default.
• W2028298308 hasAuthorship W2028298308A5019439001 @default.
• W2028298308 hasAuthorship W2028298308A5072971888 @default.
• W2028298308 hasBestOaLocation W20282983081 @default.
• W2028298308 hasConcept C134306372 @default.
• W2028298308 hasConcept C138187205 @default.
• W2028298308 hasConcept C157157409 @default.
• W2028298308 hasConcept C181104567 @default.
• W2028298308 hasConcept C192939610 @default.
• W2028298308 hasConcept C195065555 @default.
• W2028298308 hasConcept C199343813 @default.
• W2028298308 hasConcept C2524010 @default.
• W2028298308 hasConcept C2777686260 @default.
• W2028298308 hasConcept C33923547 @default.
• W2028298308 hasConcept C51955184 @default.
• W2028298308 hasConcept C5408677 @default.
• W2028298308 hasConcept C56802139 @default.
• W2028298308 hasConcept C63331456 @default.
• W2028298308 hasConcept C71924100 @default.
• W2028298308 hasConcept C78045399 @default.
• W2028298308 hasConcept C84629840 @default.
• W2028298308 hasConceptScore W2028298308C134306372 @default.
• W2028298308 hasConceptScore W2028298308C138187205 @default.
• W2028298308 hasConceptScore W2028298308C157157409 @default.
• W2028298308 hasConceptScore W2028298308C181104567 @default.
• W2028298308 hasConceptScore W2028298308C192939610 @default.
• W2028298308 hasConceptScore W2028298308C195065555 @default.
• W2028298308 hasConceptScore W2028298308C199343813 @default.
• W2028298308 hasConceptScore W2028298308C2524010 @default.
• W2028298308 hasConceptScore W2028298308C2777686260 @default.
• W2028298308 hasConceptScore W2028298308C33923547 @default.
• W2028298308 hasConceptScore W2028298308C51955184 @default.
• W2028298308 hasConceptScore W2028298308C5408677 @default.
• W2028298308 hasConceptScore W2028298308C56802139 @default.
• W2028298308 hasConceptScore W2028298308C63331456 @default.
• W2028298308 hasConceptScore W2028298308C71924100 @default.
• W2028298308 hasConceptScore W2028298308C78045399 @default.
• W2028298308 hasConceptScore W2028298308C84629840 @default.
• W2028298308 hasIssue "1" @default.
• W2028298308 hasLocation W20282983081 @default.
• W2028298308 hasOpenAccess W2028298308 @default.
• W2028298308 hasPrimaryLocation W20282983081 @default.
• W2028298308 hasRelatedWork W1124480226 @default.
• W2028298308 hasRelatedWork W118862882 @default.
• W2028298308 hasRelatedWork W185380310 @default.
• W2028298308 hasRelatedWork W2028298308 @default.
• W2028298308 hasRelatedWork W2043268301 @default.
• W2028298308 hasRelatedWork W2783731493 @default.
• W2028298308 hasRelatedWork W2808526170 @default.
• W2028298308 hasRelatedWork W3048315316 @default.
• W2028298308 hasRelatedWork W3214410636 @default.
• W2028298308 hasRelatedWork W4312762481 @default.
• W2028298308 hasVolume "139" @default.
• W2028298308 isParatext "false" @default.
• W2028298308 isRetracted "false" @default.
• W2028298308 magId "2028298308" @default.
• W2028298308 workType "article" @default.