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Functional Central Limit Theorems
2008Central limit theorems guarantee that the distributions of properly normalized sums of certain random variables are approximately normal. In many cases, however, a more detailed analysis is necessary. When testing for structural constancy in models, we might be interested in the temporal evolution of our sums.
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2003
As was pointed out in Chap. 2, the central idea in analysis is that of limit, which was introduced and studied for sequences of real numbers, i.e., for functions \(x:\mathbb{N}\rightarrow \mathbb{R}.\) In particular, the behavior of the term x n : = x(n) was studied under the assumption that the element n in the domain of our sequence was approaching ...
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As was pointed out in Chap. 2, the central idea in analysis is that of limit, which was introduced and studied for sequences of real numbers, i.e., for functions \(x:\mathbb{N}\rightarrow \mathbb{R}.\) In particular, the behavior of the term x n : = x(n) was studied under the assumption that the element n in the domain of our sequence was approaching ...
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2016
The notion of limit of a function is one of the cornerstones in Analysis. It has to do with the behaviour of a function as the variable approaches a given point, which may or may not belong to the domain of the function, as long as it is a limit point for it, also known as accumulation point.
Marco Baronti +3 more
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The notion of limit of a function is one of the cornerstones in Analysis. It has to do with the behaviour of a function as the variable approaches a given point, which may or may not belong to the domain of the function, as long as it is a limit point for it, also known as accumulation point.
Marco Baronti +3 more
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Some Useful Functions for Functional Limit Theorems
Mathematics of Operations Research, 1980Many useful descriptions of stochastic models can be obtained from functional limit theorems (invariance principles or weak convergence theorems for probability measures on function spaces). These descriptions typically come from standard functional limit theorems via the continuous mapping theorem.
Whitt, Ward, Sleeman, B. D.
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1994
Our main reason for taking up limits is to prepare the way for derivatives in the next chapter. More generally, limits provide a framework for discussing ‘indeterminate forms’ ( 0/0, 0-, 0. ∞, etc.)p1.
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Our main reason for taking up limits is to prepare the way for derivatives in the next chapter. More generally, limits provide a framework for discussing ‘indeterminate forms’ ( 0/0, 0-, 0. ∞, etc.)p1.
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1984
For real-valued functions of a real variable, the student already knows what it means for a sequence f 1, f 2, ... of functions to tend uniformly, or to tend simply, to a function f. In this chapter we study these concepts in the general setting of metric spaces.
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For real-valued functions of a real variable, the student already knows what it means for a sequence f 1, f 2, ... of functions to tend uniformly, or to tend simply, to a function f. In this chapter we study these concepts in the general setting of metric spaces.
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1995
For the definition of the limit of a function at a point, we need the notion of the accumulation point of a set, see Definition 1.76 c).
John Schmeelk +2 more
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For the definition of the limit of a function at a point, we need the notion of the accumulation point of a set, see Definition 1.76 c).
John Schmeelk +2 more
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1998
The sociological interpretation of religion by a functional approach was largely developed by social anthropologists in studying societies which used to be called ‘primitive’. The word now tends to be dropped, no doubt because it sounds patronizing, and the preferred term is ‘traditional’.
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The sociological interpretation of religion by a functional approach was largely developed by social anthropologists in studying societies which used to be called ‘primitive’. The word now tends to be dropped, no doubt because it sounds patronizing, and the preferred term is ‘traditional’.
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1983
In Chapter III we dealt with limits of real sequences. These are real-valued functions whose domains are essentially ℤ0 or ℤ1. In this chapter we treat limits of real-valued functions of a real variable whose domains are not necessarily confined to ℤ0 or ℤ1. Of special interest are functions whose domains are intervals.
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In Chapter III we dealt with limits of real sequences. These are real-valued functions whose domains are essentially ℤ0 or ℤ1. In this chapter we treat limits of real-valued functions of a real variable whose domains are not necessarily confined to ℤ0 or ℤ1. Of special interest are functions whose domains are intervals.
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Limitations of the describing function for limit cycle prediction
IEEE Transactions on Automatic Control, 2002We consider comparator-based nonlinear feedback systems, and use Tsypkin's method to develop a strategy with which to find systems with low-pass linear part for which the describing function technique erroneously predicts limit cycles. We produce an infinite set of examples of systems with very low-pass linear parts for which the describing function ...
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