Schrödinger Diffusion Processes

1 Schrödinger's View of Natural Laws.- 1.1 Most probable realizations.- 1.2 A large deviation approach.- 1.3 Prediction from past and future.- 1.4 An analogy to wave functions.- 1.5 Two representations of diffusions.- 1.6 Identification of drift.- 2 Diffusions with Singular Drift.- 2.1 Schrödinger equations.- 2.2 Non-smooth Schrödinger multipliers.- 2.3 Singular transformation of diffusions.- 2.4 Schrödinger processes.- 3 Integral and Diffusion Equations.- 3.1 Generators and transition densities.- 3.2 Feynman-Kac integral equations.- 3.3 'Killed' integral equations.- 3.4 Equivalence of solutions.- 4 Itô's Formula for Non-Smooth Functions.- 4.1 Meaning and generalization.- 4.2 Driving Brownian motion.- 4.3 Driving flows of diffeomorphisms.- 5 Large Deviations.- 5.1 Approximate Sanov property.- 5.2 Csiszar's projection and ?0-topology.- 6 Interacting Diffusion Processes.- 6.1 Eddington-Schrödinger prediction.- 6.2 Limiting distributions.- 6.3 Propagation of chaos in entropy.- 6.4 Renormalization procedures.- 6.5 Conditions on creation and killing.- 7 Schrödinger Systems.- 7.1 Non-linear integral equations.- 7.2 Product measure endomorphisms.- 7.3 A variational principle for local adjoints.- 7.4 Construction of solutions.- References.