A short course on measure and probability theories.

PÔebay, Philippe Pierre

Sandia National Laboratories

关键词: Probability;    Combustion;    Training;    Chaos Theory;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;   

DOI  :  10.2172/882320
RP-ID  :  SAND2004-8095
RP-ID  :  AC04-94AL85000
RP-ID  :  882320

美国|英语

来源: UNT Digital Library

【 摘 要 】

This brief Introduction to Measure Theory, and its applications to Probabilities, corresponds to the lecture notes of a seminar series given at Sandia National Laboratories in Livermore, during the spring of 2003. The goal of these seminars was to provide a minimal background to Computational Combustion scientists interested in using more advanced stochastic concepts and methods, e.g., in the context of uncertainty quantification. Indeed, most mechanical engineering curricula do not provide students with formal training in the field of probability, and even in less in measure theory. However, stochastic methods have been used more and more extensively in the past decade, and have provided more successful computational tools. Scientists at the Combustion Research Facility of Sandia National Laboratories have been using computational stochastic methods for years. Addressing more and more complex applications, and facing difficult problems that arose in applications showed the need for a better understanding of theoretical foundations. This is why the seminar series was launched, and these notes summarize most of the concepts which have been discussed. The goal of the seminars was to bring a group of mechanical engineers and computational combustion scientists to a full understanding of N. WIENER'S polynomial chaos theory. Therefore, these lectures notes are built along those lines, and are not intended to be exhaustive. In particular, the author welcomes any comments or criticisms.