Distributions on unbounded moment spaces and random moment sequences

Before some random moment θ, independent identically distributed random variables x1, · ··, xθ–1 with common distribution function μ (dx) appear consecutively. After the moment θ, independent random variables xθ, xθ+1, · ·· have another common distribution function f (x)μ (dx). Our information about θ can be constructed only by successively observed values of the x's.In this paper we find an optimal stopping policy by which we can maximize the probability that the quantity associated with the stopping time is the largest of all θ + m – 1 quantities for a given integer m.

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Moment Spaces and Resonance Theorems

Inequalities ◽

10.1007/978-3-642-64971-4_3 ◽

1965 ◽

pp. 97-131

Author(s):

Edwin F. Beckenbach ◽

Richard Bellman

Keyword(s):

Moment Spaces

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Moment-Based Hybrid Polynomial Chaos Method for Interval and Random Uncertain Analysis of Periodical Composite Structural-Acoustic System with Multi-Scale Parameters

International Journal of Computational Methods ◽

10.1142/s0219876220500413 ◽

2020 ◽

pp. 2050041

Author(s):

Ning Chen ◽

Jiaojiao Chen ◽

Shengwen Yin

Keyword(s):

Polynomial Chaos ◽

Random Variable ◽

Acoustic System ◽

Passenger Compartment ◽

Scale Parameters ◽

Multi Scale ◽

Arbitrary Polynomial ◽

Random Moment ◽

The Moment ◽

Probability Density Function Pdf

An interval and random moment-based arbitrary polynomial chaos method (IRMAPCM) is proposed in this paper for the analysis of periodical composite structural-acoustic systems with multi-scale uncertain-but-bounded parameters. In IRMAPCM, the response of structural-acoustic system is approximated as moment-based arbitrary polynomial chaos (maPC) expansion. IRMAPCM can construct the polynomial basis according to the moment of the random variable without knowing the Probability Density Function (PDF), which can avoid the errors introduced by estimating the PDF. Numerical examples of a hexahedral box and an automobile passenger compartment are given to investigate the effectiveness of IRMAPCM for the prediction of the sound pressure response of structural-acoustic systems.

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Geometry of moment spaces

Memoirs of the American Mathematical Society ◽

10.1090/memo/0012 ◽

1953 ◽

Vol 0 (12) ◽

pp. 0-0 ◽

Cited By ~ 45

Author(s):

S. Karlin ◽

L. S. Shapley

Keyword(s):

Moment Spaces

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Effects of ageing on responses to stepping-target displacements during walking

European Journal of Applied Physiology ◽

10.1007/s00421-020-04504-4 ◽

2020 ◽

Cited By ~ 1

Author(s):

Yajie Zhang ◽

Jeroen B. J. Smeets ◽

Eli Brenner ◽

Sabine Verschueren ◽

Jacques Duysens

Keyword(s):

Older Adults ◽

Young Adults ◽

Visual Information ◽

Muscle Activation ◽

Gluteus Medius ◽

Swing Phase ◽

Motor Systems ◽

Lateral Direction ◽

Activity Data ◽

Random Moment

Abstract Purpose Human sensory and motor systems deteriorate with age. When walking, older adults may therefore find it more difficult to adjust their steps to new visual information, especially considering that such adjustments require control of balance as well as of foot trajectory. Our study investigates the effects of ageing on lower limb responses to unpredictable target shifts. Methods Participants walked on a treadmill with projected stepping targets that occasionally shifted in the medial or lateral direction. The shifts occurred at a random moment during the early half of the swing phase of either leg. Kinematic, kinetic and muscle activity data were collected. Results Older adults responded later and corrected for a smaller proportion of the shift than young adults. The order in which muscle activation changed was similar in both groups, with responses of gluteus medius and semitendinosus from about 120 to 140 ms after the shift. Most muscles responded slightly later to lateral target shifts in the older adults than in the young adults, but this difference was not observed for medial target shifts. Ageing delayed the behavioural responses more than it did the electromyographic (EMG) responses. Conclusions Our study suggests that older adults can adjust their walking to small target shifts during the swing phase, but not as well as young adults. Furthermore, muscle strength probably plays a substantial role in the changes in online adjustments during ageing.

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Large Deviations on Moment Spaces

Electronic Journal of Probability ◽

10.1214/ejp.v10-202 ◽

2005 ◽

Vol 10 (0) ◽

pp. 662-690 ◽

Cited By ~ 9

Author(s):

Li-Vang Lozada-Chang

Keyword(s):

Large Deviations ◽

Moment Spaces

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More bounds on the expectation of a convex function of a random variable

Journal of Applied Probability ◽

10.2307/3212616 ◽

1972 ◽

Vol 9 (4) ◽

pp. 803-812 ◽

Cited By ~ 42

Author(s):

Ben-Tal A. ◽

E. Hochman

Keyword(s):

Convex Function ◽

Upper Bound ◽

Random Variable ◽

Independent Random Variables ◽

Multivariate Distributions ◽

Absolute Deviation ◽

Additional Information ◽

Wait And See ◽

The Mean ◽

Moment Spaces

Jensen gave a lower bound to Eρ(T), where ρ is a convex function of the random vector T. Madansky has obtained an upper bound via the theory of moment spaces of multivariate distributions. In particular, Madansky's upper bound is given explicitly when the components of T are independent random variables. For this case, lower and upper bounds are obtained in the paper, which uses additional information on T rather than its mean (mainly its expected absolute deviation about the mean) and hence gets closer to Eρ(T).The importance of having improved bounds is illustrated through a nonlinear programming problem with stochastic objective function, known as the “wait and see” problem.

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