Conditional Expectation and Martingales
نویسنده
چکیده
These notes are intended to introduce concentration inequalities for martingales with bounded increments. The final section also provides a gentle introduction to conditional expectation based on sigma fields. In contrast to providing a firm foundation for measure-theoretic probability, the primary goal is to introduce the language and intuition used in the study of martingales. The presentation is based on [1] but adds a few examples and details.
منابع مشابه
Measure-Free Martingales with Application to Classical Martingales
The aim of this work is to give a summary of some of the known properties of sets of measure-free martingales in vector lattices and Banach spaces. In particular, we consider the relationship between such sets of martingales and the ranges of the underlying filtration of conditional expectation operators.
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متن کاملProbability Theory : STAT 310 / MATH 230 ; September 12 , 2010 Amir
Contents Preface 5 Chapter 1. Probability, measure and integration 7 1.1. Probability spaces, measures and σ-algebras 7 1.2. Random variables and their distribution 18 1.3. Integration and the (mathematical) expectation 30 1.4. Independence and product measures 54 Chapter 2. Asymptotics: the law of large numbers 71 2.1. Weak laws of large numbers 71 2.2. The Borel-Cantelli lemmas 77 2.3. Strong...
متن کاملConditional Expectation and Martingales
This is a set of very hurriedly compiled notes. It has not been proof-checked and is likely to have some errors. These, though, should be minor errors and maybe cleared up by referring to the relevant texts. The texts that have been used in the preparation of the notes are Feller; Grimmett and Stirzaker; Goswami and Rao; David Williams; and Mitzenmacher and Upfal. The purpose behind the notes i...
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From a general deenition of nonlinear expectations, viewed as operators preserving monotonicity and constants, we derive, under rather general assumptions, the notions of conditional nonlinear expectation and nonlinear martingales. We prove that any such nonlinear martingale can be represented as the solution of a backward stochastic equation, and in particular admits continuous paths. In other...
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تاریخ انتشار 2015