Geometry and Invariance in Stochastic Dynamics : Verona, Italy, March 25-29, 2019 / edited by Stefania Ugolini, Marco Fuhrman, Elisa Mastrogiacomo, Paola Morando, Barbara Rüdiger.

Format:

Book

Author/Creator:

Ugolini, Stefania, author.

Series:

Springer Proceedings in Mathematics & Statistics, 2194-1017 ; 378

Language:

English

Subjects (All):

Probabilities.

Mathematical physics.

Mechanics.

Mathematical analysis.

Probability Theory.

Mathematical Physics.

Classical Mechanics.

Analysis.

Local Subjects:

Probability Theory.

Mathematical Physics.

Classical Mechanics.

Analysis.

Physical Description:

1 online resource (273 pages)

Edition:

1st ed. 2021.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2021.

Summary:

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.

Contents:

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. .

Other Format:

Print version: Ugolini, Stefania Geometry and Invariance in Stochastic Dynamics

ISBN:

3-030-87432-X