Some recent developments on Lie symmetry analysis of stochastic differential equations

DOI10.1007/978-3-030-87432-2_1zbMath1499.60176OpenAlexW4211093778MaRDI QIDQ2107405

Francesco C. De Vecchi, Sergio A. Albeverio

Publication date: 1 December 2022

Full work available at URL: https://doi.org/10.1007/978-3-030-87432-2_1

zbMATH Keywords

stochastic differential equationsKolmogorov equationLie symmetry analysisNoether stochastic theorem

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Group actions and symmetry properties (58D19) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Research exposition (monographs, survey articles) pertaining to probability theory (60-02) Jump processes on general state spaces (60J76)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A weak approach to the stochastic deformation of classical mechanics
• Symmetries in the stochastic calculus of variations
• Symmetry groups and translation invariant representations of Markov processes
• The Noether theorems. Invariance and conservation laws in the twentieth century. Transl. from the French by Bertram E. Schwarzbach
• Markov processes invariant under a Lie group action
• Applications of symmetry methods to partial differential equations
• Symmetry groups of Markov processes
• Symmetries of Itô and Stratonovich dynamical systems and their conserved quantities
• Emergence of the theory of Lie groups. An essay in the history of mathematics 1869--1926
• Solvable structures for evolution PDEs admitting differential constraints
• Existence of invariant manifolds for stochastic equations in infinite dimension
• Geometric and symmetry properties of a nondegenerate diffusion process
• Conserved quantities and symmetry for stochastic dynamical systems
• Reduction of the Zakai equation by invariance group techniques
• Random transformations and invariance of semimartingales on Lie groups
• Weak symmetries of stochastic differential equations driven by semimartingales with jumps
• The geometry of differential constraints for a class of evolution PDEs
• An intrinsic calculus of variations for functionals of laws of semi-martingales
• A symmetry-adapted numerical scheme for SDEs
• Symmetry of stochastic non-variational differential equations
• Momentum maps and stochastic Clebsch action principles
• Reduction and reconstruction of stochastic differential equations via symmetries
• A Note on a Result of Liptser-Shiryaev
• Symmetries of stochastic differential equations: A geometric approach
• On the definition of an admitted Lie group for stochastic differential equations with multi-Brownian motion
• Symmetries of systems of stochastic differential equations with diffusion matrices of full rank
• REDUCTION, RECONSTRUCTION, AND SKEW-PRODUCT DECOMPOSITION OF SYMMETRIC STOCHASTIC DIFFERENTIAL EQUATIONS
• A note on the symmetry group and perturbation algebra of a parabolic partial differential equation
• Invariant variation problems
• Iterated Random Functions
• Finite-Dimensional Filters. Part I: The Wei--Norman Technique
• Finite-Dimensional Filters. Part II: Invariance Group Techniques
• Lie-point symmetries and stochastic differential equations: II
• Lie point symmetries of Stratonovich stochastic differential equations
• Random Lie symmetries of Itô stochastic differential equations
• Lie-point symmetries and stochastic differential equations
• Stochastic deformation of integrable dynamical systems and random time symmetry
• The group classification of a scalar stochastic differential equation
• Variational principles for stochastic fluid dynamics
• W-symmetries of Ito stochastic differential equations
• Symmetries of first‐order stochastic ordinary differential equations revisited
• Random Lie-point symmetries of stochastic differential equations
• Integration of the stochastic logistic equation via symmetry analysis
• Symmetry and integrability for stochastic differential equations
• The Research Program of Stochastic Deformation (with a View Toward Geometric Mechanics)
• Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries
• Symmetries and differential equations

This page was built for publication: Some recent developments on Lie symmetry analysis of stochastic differential equations