{"product_id":"brownian-motion-and-its-applications-to-mathematical-analysis-ecole-dete-de-probabilites-de-saint-flour-xliii-2013-9783319043937","title":"Brownian Motion and its Applications to Mathematical Analysis: École d'Été de Probabilités de Saint-Flour XLIII – 2013","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThese 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.\u003c\/p\u003e\u003cp\u003eThe 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.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. 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.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":51742928142679,"sku":"9783319043937","price":999.99,"currency_code":"GBP","in_stock":false}],"url":"https:\/\/bookcurl.com\/products\/brownian-motion-and-its-applications-to-mathematical-analysis-ecole-dete-de-probabilites-de-saint-flour-xliii-2013-9783319043937","provider":"Book Curl","version":"1.0","type":"link"}