Mimicking martingales
نویسندگان
چکیده
منابع مشابه
Continuous Martingales and Local Martingales
Throughout these notes, (Ω,F ,P ) will be a probability space and F := {Ft }t∈J a filtration indexed by J , where J is an interval, usually J = [0,∞). The filtration F is said to be complete if each Ft contains all sets of measure 0, and is right-continuous if Ft =∩s>t Fs . A standard filtration is a filtration that is both complete and right-continuous. A stochastic process {X t }t≥0 defined o...
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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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We construct a class of nonnegative martingale processes that oscillate indefinitely with high probability. For these processes, we state a uniform rate of the number of oscillations for a given magnitude and show that this rate is asymptotically close to the theoretical upper bound. These bounds on probability and expectation of the number of upcrossings are compared to classical bounds from t...
متن کاملIntroduction to Martingales
We’ve already encountered and used martingales in this course to help study the hitting-times of Markov processes. Informally a martingale is simply a stochastic process Mt defined on some probability space (Ω,F ,P) that is “conditionally constant,” i.e., whose predicted value at any future time s > t is the same as its present value at the time t of prediction. The set T of possible indices t ...
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Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the symmetric group on transpositions. A generalization of these results is given for Jack measure on partitions. We also give a probabilistic proof of a result of Burn...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2016
ISSN: 1050-5164
DOI: 10.1214/15-aap1147