Schroedinger diffusion processes

Cover......Page 1
Schrödinger Diffusion Processes......Page 4
ISBN 3764353864  ISBN 0817653864......Page 5
Contents......Page 6
Preface......Page 8
1 Schrödinger\'s View of Natural Laws......Page 10
1.1 Most probable realizations......Page 11
1.2 A large deviation approach......Page 15
1.3 Prediction from past and future......Page 17
1.4 An analogy to wave functions......Page 21
1.5 Two representations of diffusions......Page 24
1.6 Identification of drift......Page 27
2 Diffusions with Singular Drift......Page 32
2.1 Schrödinger equations......Page 33
2.2 Non-smooth Schrödinger multipliers......Page 38
2.3 Singular transformation of diffusions......Page 42
2.4 Schrödinger processes......Page 55
3.1 Generators and transition densities......Page 64
3.2 Feynman-Kac integral equations......Page 66
3.3 \'Killed\' integral equations......Page 74
3.4 Equivalence of solutions......Page 79
4.1 Meaning and generalization......Page 86
4.2 Driving Brownian motion......Page 88
4.3 Driving flows of diffeomorphisms......Page 91
5 Large Deviations......Page 100
5.1 Approximate Sanov property......Page 101
5.2 Csiszar\'s projection and To-topology......Page 105
6 Interacting Diffusion Processes......Page 124
6.1 Eddington-Schrödinger prediction......Page 125
6.2 Limiting distributions......Page 126
6.3 Propagation of chaos in entropy......Page 132
6.4 Renormalization procedures......Page 151
6.5 Conditions on creation and killing......Page 155
7 Schrödinger Systems......Page 160
7.1 Non-linear integral equations......Page 161
7.2 Product measure endomorphisms......Page 164
7.3 A variational principle for local adjoints......Page 170
7.4 Construction of solutions......Page 180
References......Page 184
Index......Page 194