Brownian Motion and its Applications to Mathematical Analysis École d'Été de Probabilités de Saint-Flour XLIII – 2013 /

• Κύριος συγγραφέας: Burdzy, Krzysztof (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Σειρά: Lecture Notes in Mathematics, 2106
• Θέματα: Mathematics.; Partial differential equations.; Potential theory (Mathematics).; Probabilities.; Probability Theory and Stochastic Processes.; Partial Differential Equations.; Potential Theory.

These lecture notes provide an introduction to the applications of Brownian motion to analysis and, more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, su...

Πίνακας περιεχομένων:

• 1. Brownian motion
• 2. Probabilistic proofs of classical theorems
• 3. Overview of the "hot spots" problem
• 4. Neumann eigenfunctions and eigenvalues
• 5. Synchronous and mirror couplings
• 6. Parabolic boundary Harnack principle
• 7. Scaling coupling
• 8. Nodal lines
• 9. Neumann heat kernel monotonicity
• 10. Reflected Brownian motion in time dependent domains.