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 $\{ Z_s: 0 \leq s \lt t\}$ lies on one side of $\mathcal L$ and the trace of $\{Z_s: t \lt s \lt 1\}$ lies on the other side of $\mathcal L$. In this volume, the authors provide a solution, discuss related works, and present a number of open problems.

Cutting Brownain Paths (Memoirs of the American Mathematical Society)

Science & Math

Bass, Richard F.

BURDZY, KRZYSZTOF

Mathematics

Amer Mathematical Society

Resonance examines some building blocks of epistemology as a prelude to the careful analysis of the foundations of probability. The concept of resonance is introduced to shed light on the philosophical problems of induction, consciousness, intelligence and free will. The same concept is later applied to provide support for a new philosophical theory of probability.Although based on existing ideas and theories, the epistemological concept of resonance is investigated for the first time in this book. The best-known philosophical theories of probability, frequency and subjective, are shown to be unrealistic and dissociated from the two main branches of statistics: frequency statistics and Bayesian statistics.Written in an accessible style, this book can be enjoyed by philosophers, statisticians and mathematicians, and also by anyone looking to expand their understanding of the disciplines of epistemology and probability.

RESONANCE: FROM PROBABILITY TO EPISTEMOLOGY AND BACK

Politics & Social Sciences

Philosophy

World Scientific Pub Co Inc

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.

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

Springer

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. The new laws are simple, intuitive and, last but not least, they agree well with the contents of current textbooks on probability. Another major new claim is that the "frequency statistics" has nothing in common with the "frequency philosophy of probability," contrary to popular belief. Similarly, contrary to the general perception, the "Bayesian statistics" shares nothing in common with the "subjective philosophy of probability."The book is non-partisan on the scientific side -- it is supportive of both frequency statistics and Bayesian statistics. On the other hand, it contains well-documented and thoroughly-explained criticisms of the frequency and subjective philosophies of probability. Short reviews of other philosophical theories of probability and basic mathematical methods of probability and statistics are incorporated. The book includes substantial chapters on decision theory and teaching probability, and it is easily accessible to the general audience.

SEARCH FOR CERTAINTY, THE: ON THE CLASH OF SCIENCE AND PHILOSOPHY OF PROBABILITY

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Books by BURDZY, KRZYSZTOF

See the best price to sell, buy, or rent books by BURDZY, KRZYSZTOF. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Cutting Brownain Paths (Memoirs of the American Mathematical Society)

RESONANCE: FROM PROBABILITY TO EPISTEMOLOGY AND BACK

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

SEARCH FOR CERTAINTY, THE: ON THE CLASH OF SCIENCE AND PHILOSOPHY OF PROBABILITY