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Amarts: A class of asymptotic martingales a. Discrete parameter
Journal of Multivariate Analysis, 1976 AbstractA sequence (Xn) of random variables adapted to an ascending (asc.) sequence Fn of σ-algebras is an amart iff EXτ converges as τ runs over the set T of bounded stopping times. An analogous definition is given for a descending (desc.) sequence Fn. A systematic treatment of amarts is given.
Edgar, Gerald A., Sucheston, Louis
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Book Review: Discrete-parameter martingales [PDF]
Bulletin of the American Mathematical Society, 1976 openaire +1 more source
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Discrete Parameter Martingales
Indian Statistical Institute Series, 2018In this chapter, we will discuss martingales indexed by integers (mostly positive integers) and obtain basic inequalities on martingales and other results which are the basis of most of the developments in later chapters on stochastic integration. We will begin with a discussion on conditional expectation and then on filtration—two notions central to ...
Rajeeva L Karandikar +2 more
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DISCRETE-TIME MARTINGALES WITH SPATIAL PARAMETERS
Stochastic Analysis and Applications, 2002Our analysis of a certain stochastic difference equation driven by a martingale k↦M(x,k) that depends on a spatial parameter x∈R d requires some regularity properties of the underlying martingale be satisfied. Because of their independent interest, we present these regularity properties in this article.
Bo Zhang, D. Kannan
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Martingale with Discrete Parameter
2020Let \(\mathbf{T}\) be an ordered set. We only consider the case that \(\mathbf{T}\) is a subset of \([-\infty , \infty ]\) in this book. In almost all cases, \(\mathbf{T}\) is \(\{ 0,1, 2,\ldots ,m\} ,\) \(m\geqq 1,\) or \(\mathbf{Z}_{\geqq 0}\) \(=\{ 0, 1,2, \ldots \} ,\) or [0, T], \(T>0,\) or \([0,\infty ),\) although we consider the case that ...
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Discrete Parameter Martingales
1992The concept of a martingale introduced in Section 1.5 of Chapter 1 [see (1.5.19)] was defined in terms of the conditional expectation with respect to a σ-algebra. In this section, we will explore briefly some basic properties of this conditional expectation, which are needed in this chapter. We begin with some definitions.
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Discrete-Parameter Martingales
2002In this chapter we develop the basic theory of multiparameter martingales indexed by a countable subset of ℝ + N , usually or ℕ N . As usual, ℕ 0 N . As usual, ℕ= {1, 2,…}, ℕ0 = {0,1, 2,…}, and N denotes a fixed positive integer.
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Discrete-Parameter Martingales.
Journal of the Royal Statistical Society. Series A (General), 1976J. F. C. Kingman, Jacques Neveu
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