Radically Elementary Probability Theory (eBook)

Edward Nelson (Autor)

eBook Download: PDF

2016
Princeton University Press (Verlag)
978-1-4008-8214-4 (ISBN)

Infos

Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: Abraham Robinson • absolute value • Addition • Algebra of random variables • Almost surely • Axiom • axiomatic system • Borel set • bounded function • Cantor's Diagonal Argument • Cardinality • Cartesian Product • central limit theorem • Chebyshev's inequality • Compact space • Contradiction • Convergence of random variables • corollary • correlation coefficient • counterexample • Dimension • Dimension (vector space) • Division by zero • Elementary function • estimation • existential quantification • Family of sets • Finite set • hyperplane • idealization • Independence (probability theory) • Indicator function • Infinitesimal • Internal Set Theory • Joint probability distribution • law of large numbers • Linear Function • Martingale (probability theory) • Mathematical Induction • mathematician • Mathematics • Measure (mathematics) • N0 • Natural number • non-standard analysis • Norm (mathematics) • Orthogonal complement • Parameter • path space • predictable process • Probability • Probability Distribution • probability measure • Probability space • Probability Theory • Product topology • Projection (linear algebra) • quadratic variation • Random Variable • real number • Requirement • scientific notation • Sequence • Set (mathematics) • Significant figures • Special case • standard deviation • Statistical Mechanics • Stochastic process • Subalgebra • Subset • Summation • Theorem • theory • total variation • Transfer principle • Transfinite number • Trigonometric Functions • Upper and lower bounds • Variable (mathematics) • Variance • Vector Space • W0 • Wiener process • Without loss of generality
• ISBN-10: 1-4008-8214-1 / 1400882141
• ISBN-13: 978-1-4008-8214-4 / 9781400882144