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＜電子ブック＞
Geometry and Invariance in Stochastic Dynamics : Verona, Italy, March 25-29, 2019 / edited by Stefania Ugolini, Marco Fuhrman, Elisa Mastrogiacomo, Paola Morando, Barbara Rüdiger
(Springer Proceedings in Mathematics & Statistics. ISSN:21941017 ; 378)

版	1st ed. 2021.
出版者	Cham : Springer International Publishing : Imprint: Springer
出版年	2021
本文言語	英語
大きさ	XIV, 265 p. 18 illus., 13 illus. in color : online resource
著者標目	Ugolini, Stefania editor Fuhrman, Marco editor Mastrogiacomo, Elisa editor Morando, Paola editor Rüdiger, Barbara editor SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Mathematical physics LCSH:Mechanics LCSH:Mathematical analysis FREE:Probability Theory FREE:Mathematical Physics FREE:Classical Mechanics FREE:Analysis
一般注記	Albeverio, S., De Vecchi, F.C.: Some recent developments on Lie Symmetry analysis of stochastic differential equations -- Applebaum, D., Ming, L.: Markov processes with jumps on manifolds and Lie groups -- Cordoni, F., Di Persio, L.: Asymptotic expansion for a Black-Scholes model with small noise stochastic jump diffusion interest rate -- Cruzeiro, A.B., Zambrini, J.C.: Stochastic geodesics -- DeVecchi, F.C., Gubinelli, M.: A note on supersymmetry and stochastic differential equations -- Ebrahimi-Fard, K, Patras, F.: Quasi shuffle algebras in non-commutative stochastic calculus -- Elworthy, K.D.: Higher order derivatives of heat semigroups on spheres and Riemannian symmetric spaces -- Gehringer, J., Li, X.M.: Rough homogenisation with fractional dynamics -- Holm, D.D., Luesink, E.: Stochastic geometric mechanics with diffeomorphisms -- Izydorczyk, L., Oudjane, N., Russo, F.: McKean Feynman-Kac probabilistic representations of non linear partial differential equations -- Lescot, P., Valade, L.: Bernestein processes, isovectors and machanics -- Marinelli, C., Scarpa, L.: On the positivity of local mild solutions to stochastic evolution equations -- Privault, N.: Invariance of Poisson point processes by moment identities with statistical applications. This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling HTTP:URL=https://doi.org/10.1007/978-3-030-87432-2

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