Stochastic Ordinary and Stochastic Partial Differential Equations

Part I. From Microscopic Dynamics to Mesoscopic Kinematics

1. Heuristics: Microscopic Model and Space—Time Scales

2. Deterministic Dynamics in a Lattice Model and a Mesoscopic (Stochastic) Limit

3. Proof of the Mesoscopic Limit Theorem

Part II. Mesoscopic A: Stochastic Ordinary Differential Equations

4. Stochastic Ordinary Differential Equations: Existence, Uniqueness, and Flows Properties

5. Qualitative Behavior of Correlated Brownian Motions

6. Proof of the Flow Property

7. Comments on SODEs: A Comparison with Other Approaches

Part III. Mesoscopic B: Stochastic Partial Differential Equations

8. Stochastic Partial Differential Equations: Finite Mass and Extensions

9. Stochastic Partial Differential Equations: Infinite Mass

10. Stochastic Partial Differential Equations:Homogeneous and Isotropic Solutions

11. Proof of Smoothness, Integrability, and Itô’s Formula

12. Proof of Uniqueness

13. Comments on Other Approaches to SPDEs

Part IV. Macroscopic: Deterministic Partial Differential Equations

14. Partial Differential Equations as a Macroscopic Limit

Part V. General Appendix

15. Appendix

DRM-restrictions

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Keywords: MATHEMATICS / General MAT000000