SYMPLECTIC STRUCTURES ON STATISTICAL MANIFOLDS
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Publication:3173416
DOI10.1017/S1446788711001285zbMath1226.53083OpenAlexW2085461304MaRDI QIDQ3173416
Publication date: 10 October 2011
Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s1446788711001285
Geometric probability and stochastic geometry (60D05) Momentum maps; symplectic reduction (53D20) Statistical aspects of information-theoretic topics (62B10)
Related Items (12)
Affine geometric description of thermodynamics ⋮ Statistical manifolds with almost quaternionic structures and quaternionic Kähler-like statistical submersions ⋮ Conformally-projectively flat trans-Sasakian statistical manifolds ⋮ Geometry from divergence functions and complex structures ⋮ Statistical structures in almost paracontact geometry ⋮ Maps on statistical manifolds exactly reduced from the Perron-Frobenius equations for solvable chaotic maps ⋮ Interaction of Codazzi couplings with (para-)Kähler geometry ⋮ Complex affine distributions ⋮ Almost product structures on statistical manifolds and para-Kähler-like statistical submersions ⋮ Submanifold Theory in Holomorphic Statistical Manifolds ⋮ Almost cosympletic statistical manifolds ⋮ Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium statistical mechanics
Cites Work
- Completely integrable gradient systems on the manifolds of Gaussian and multinomial distributions
- Strong symplectic structures on spaces of probability measures with positive density function.
- Exponential statistical manifold
- Gradient systems associated with probability distributions
- Statistics, yokes and symplectic geometry
- Symplectic manifolds and their Lagrangian submanifolds
- Die Fisher-Information und symplektische Strukturen
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