LEADER 05129nam 22006855 450 001 9910544859003321 005 20260119145604.0 010 $a3-030-87432-X 024 7 $a10.1007/978-3-030-87432-2 035 $a(MiAaPQ)EBC6885899 035 $a(Au-PeEL)EBL6885899 035 $a(CKB)21167809100041 035 $a(PPN)260827703 035 $a(DE-He213)978-3-030-87432-2 035 $a(EXLCZ)9921167809100041 100 $a20220209d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometry and Invariance in Stochastic Dynamics $eVerona, Italy, March 25-29, 2019 /$fedited by Stefania Ugolini, Marco Fuhrman, Elisa Mastrogiacomo, Paola Morando, Barbara Rüdiger 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (273 pages) 225 1 $aSpringer Proceedings in Mathematics & Statistics,$x2194-1017 ;$v378 311 08$aPrint version: Ugolini, Stefania Geometry and Invariance in Stochastic Dynamics Cham : Springer International Publishing AG,c2022 9783030874315 327 $aAlbeverio, 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. . 330 $aThis book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie?s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling. 410 0$aSpringer Proceedings in Mathematics & Statistics,$x2194-1017 ;$v378 606 $aProbabilities 606 $aMathematical physics 606 $aMechanics 606 $aMathematical analysis 606 $aProbability Theory 606 $aMathematical Physics 606 $aClassical Mechanics 606 $aAnalysis 606 $aEquacions diferencials estocàstiques$2thub 608 $aCongressos$2thub 608 $aLlibres electrònics$2thub 615 0$aProbabilities. 615 0$aMathematical physics. 615 0$aMechanics. 615 0$aMathematical analysis. 615 14$aProbability Theory. 615 24$aMathematical Physics. 615 24$aClassical Mechanics. 615 24$aAnalysis. 615 7$aEquacions diferencials estocàstiques 676 $a519.2 676 $a519.22 702 $aUgolini$b Stefania 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910544859003321 996 $aGeometry and invariance in stochastic dynamics$92917806 997 $aUNINA