Results 261 to 270 of about 3,675,924 (300)

Random Variables, Elements, and Measurable Maps

2005
In this chapter, we will precisely define a random variable. A random variable is a real valued function with domain Ω which has an extra property called measurability that allows us to make probability statements about the random variables.
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On the second role of the random element in minimization

Contemporary Clinical Trials, 2010
Although the main reason for adding a random element at every step of minimization procedure is to reduce predictability of the upcoming treatment assignments in single-center open-label trials, there is another reason for its use, applicable to double-blind trials.
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Strong previsions of random elements

Statistical Methods & Applications, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
BERTI P., REGAZZINI, EUGENIO, RIGO, PIETRO   +2 more
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Convergence in Law of Random Elements and Random Sets

1998
Throughout this paper, we let T denote a fixed topological space (not necessarily Hausdorff) and we let (Ω, F, P) and (ϒ, A, Q) denote two fixed probability spaces. We let (E,E*,E *) denote the P-expectation, the upper and the lower P-expectation. Similarly, we let (E,E*,E*) denote the Q-expectation, the upper and the lower Q-expectation. Recall that a
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Quantum Random Active Element Machine

2013
In [4], a computational procedure (Procedure 2) - combining quantum randomness and the active element machine (AEM) [5] - executes a universal Turing machine with Turing incomputable firing patterns. The procedure emulates any digital computer program so its computational steps are incomprehensible to an external observer.
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A Finite Element Method for Random Differential Equations with Random Coefficients

SIAM Journal on Numerical Analysis, 1979
A finite element method is derived for solving equations of the following type \[ - (p(x)u'(x,\omega ))' + (q(x) + r(x)\lambda (\omega ))^2 u(x,\omega ) = f(x,\omega ),\quad 0 \leqq x \leqq l,\] with boundary conditions $u(0,\omega ) \equiv u(l,\omega ) \equiv 0$ where (i) $0 < p \in C^1 [0,l]$; (ii) $q,r \in C[0,l]$; (iii) $f(x,\omega ) = B'(x,\omega )
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Series of independent random elements

1997
This chapter is entirely devoted to series of independent random elements in separable F-spaces. Sections 1.1 and 1.2 are preliminary. The equivalence of strong and weak almost sure convergence of series of independent symmetric summands (a generalization of the Ito-Nisio theorem) is considered in Section 1.3.
Valery Buldygin, Serguei Solntsev
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Sums of Independent Random Elements

1987
Independence is one of the most important notions of the probability theory, and series of independent random elements in Banach spaces are an interesting object in themselves but also have applications in other areas of mathematics, in particular, in the geometric theory of Banach spaces.
N. N. Vakhania, V. I. Tarieladze, S. A. Chobanyan   +2 more
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On convergence for series of random elements

Nonlinear Analysis: Theory, Methods & Applications, 2001
Hu, Tien-Chung, Wang, Chunnan
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A stochastic finite element scheme for solving partial differential equations defined on random domains

Computer Methods in Applied Mechanics and Engineering, 2023
Michael Beer, Marcos Valdebenito
exaly