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Stochastic Calculus in Manifolds

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概要 Addressed to both pure and applied probabilitists, including graduate students, this text is a pedagogically-oriented introduction to the Schwartz-Meyer second-order geometry and its use in stochastic... calculus. P.A. Meyer has contributed an appendix: "A short presentation of stochastic calculus" presenting the basis of stochastic calculus and thus making the book better accessible to non-probabilitists also. No prior knowledge of differential geometry is assumed of the reader: this is covered within the text to the extent. The general theory is presented only towards the end of the book, after the reader has been exposed to two particular instances - martingales and Brownian motions - in manifolds. The book also includes new material on non-confluence of martingales, s.d.e. from one manifold to another, approximation results for martingales, solutions to Stratonovich differential equations. Thus this book will prove very useful to specialists and non-specialists alike, as a self-contained introductory text or as a compact reference.続きを見る
目次 I. Real semimartingales and stochastic integrals
II. Some vocabulary from differential geometry
III. Manifold-valued semimartingales and their quadratic variation
IV. Connections and martingales
V. Riemannian manifolds and Brownian motions
VI. Second order vectors and forms
VII. Stratonovich and Itô integrals of first order forms
VIII. Parallel transport and moving frame
Appendix: A short presentation of stochastic calculus.
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登録日 2020.06.27
更新日 2020.06.28