TY - BOOK
AU - Burdzy, Krzysztof.
ED - SpringerLink (Online service)
TI - Brownian Motion and its Applications to Mathematical Analysis: École d'Été de Probabilités de Saint-Flour XLIII – 2013
T2 - Lecture Notes in Mathematics,
SN - 9783319043
AV - QA273.A1-274.9
U1 - 519.2 23
PY - 2014///
CY - Cham
PB - Springer International Publishing, Imprint: Springer
KW - Mathematics
KW - Differential equations, partial
KW - Potential theory (Mathematics)
KW - Distribution (Probability theory)
KW - Probability Theory and Stochastic Processes
KW - Partial Differential Equations
KW - Potential Theory
N1 - 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
N2 - 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, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in "deterministic" fields of mathematics. The notes include a brief review of Brownian motion and a section on probabilistic proofs of classical theorems in analysis. The bulk of the notes are devoted to recent (post-1990) applications of stochastic analysis to Neumann eigenfunctions, Neumann heat kernel and the heat equation in time-dependent domains
UR - http://dx.doi.org/10.1007/978-3-319-04394-4
ER -