Product Description: 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...read more

Product Description: This volume represents a radical departure from the current philosophical duopoly in the area of foundations of probability, that is, the frequency and subjective theories. One of the main new ideas is a set of scientific laws of probability...read more

Product Description: A long open problem in probability theory has been the following: Can the graph of planar Brownian motion be split by a straight line? Let $Z_t$ be two-dimensional Brownian motion. Say that a straight line $\mathcal L$ is a cut line if there exists a time $t \in (0,1)$ such that the trace of $\{Z_s: 0\leq ...read more (view table of contents, read Amazon.com's description)