TY - BOOK ID - 5450591 TI - Lectures on probability theory and statistics : Ecole d'eté de probabilités de Saint-Flour XXXIII - 2003 AU - Dembo, Amir AU - Picard, Jean AU - Funaki, Tadahisa PY - 2005 SN - 9783540260691 3540260692 3540315373 PB - Berlin, Heidelberg : Springer, DB - UniCat KW - Probabilities. KW - Mathematical statistics. KW - Probabilités KW - Statistique mathématique KW - Mathematics. KW - Differential equations, partial. KW - Potential theory (Mathematics). KW - Distribution (Probability theory). KW - Statistics. KW - Probability Theory and Stochastic Processes. KW - Measure and Integration. KW - Potential Theory. KW - Statistics for Engineering, Physics, Computer Science, Chemistry & Geosciences. KW - Partial Differential Equations. KW - Mathematical Statistics KW - Mathematics KW - Physical Sciences & Mathematics KW - Statistical analysis KW - Statistical data KW - Statistical methods KW - Statistical science KW - Distribution functions KW - Frequency distribution KW - Green's operators KW - Green's theorem KW - Potential functions (Mathematics) KW - Potential, Theory of KW - Partial differential equations KW - Math KW - Measure theory. KW - Partial differential equations. KW - Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. KW - Econometrics KW - Mathematical analysis KW - Mechanics KW - Science KW - Probability KW - Statistical inference KW - Combinations KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Lebesgue measure KW - Measurable sets KW - Measure of a set KW - Algebraic topology KW - Integrals, Generalized KW - Measure algebras KW - Rings (Algebra) KW - Distribution (Probability theory. KW - Characteristic functions KW - Probabilities KW - Statistics . KW - Distribution (Probability theory) UR - https://www.unicat.be/uniCat?func=search&query=sysid:5450591 AB - This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki’s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called abla varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques. ER -