scholarly journals Positive Dependence of Signals

2010 ◽  
Vol 47 (3) ◽  
pp. 893-897 ◽  
Author(s):  
Michel Denuit
Keyword(s):  
Conditional Expectation ◽  
Conditional Variance ◽  
Sufficient Condition ◽  
Convex Order ◽  
Positive Dependence ◽  
Increasing Convex Order ◽  
Quantity Of Interest ◽  
Conditional Expectations ◽  
Special Case

In this paper we further investigate the problem considered by Mizuno (2006) in the special case of identically distributed signals. Specifically, we first propose an alternative sufficient condition of crossing type for the convex order to hold between the conditional expectations given signal. Then, we prove that the bivariate (2,1)-increasing convex order ensures that the conditional expectations are ordered in the convex sense. Finally, the L2 distance between the quantity of interest and its conditional expectation given signal (or expected conditional variance) is shown to decrease when the strength of the dependence increases (as measured by the (2,1)-increasing convex order).

scholarly journals Positive Dependence of Signals

2010 ◽  
Vol 47 (03) ◽  
pp. 893-897 ◽  
Author(s):  
Michel Denuit
Keyword(s):  
Conditional Expectation ◽  
Conditional Variance ◽  
Sufficient Condition ◽  
Convex Order ◽  
Positive Dependence ◽  
Increasing Convex Order ◽  
Quantity Of Interest ◽  
Conditional Expectations ◽  
Special Case

In this paper we further investigate the problem considered by Mizuno (2006) in the special case of identically distributed signals. Specifically, we first propose an alternative sufficient condition of crossing type for the convex order to hold between the conditional expectations given signal. Then, we prove that the bivariate (2,1)-increasing convex order ensures that the conditional expectations are ordered in the convex sense. Finally, the L 2 distance between the quantity of interest and its conditional expectation given signal (or expected conditional variance) is shown to decrease when the strength of the dependence increases (as measured by the (2,1)-increasing convex order).

scholarly journals A relation between positive dependence of signal and the variability of conditional expectation given signal

2006 ◽  
Vol 43 (04) ◽  
pp. 1181-1185 ◽  
Author(s):  
Toshihide Mizuno
Keyword(s):  
Conditional Expectation ◽  
Marginal Distribution ◽  
Stochastic Order ◽  
Random Variable ◽  
Sufficient Condition ◽  
Conditional Distributions ◽  
Convex Order ◽  
Positive Dependence ◽  
Dispersive Order ◽  
Conditional Expectations

Let S 1 and S 2 be two signals of a random variable X, where G 1(s 1 ∣ x) and G 2(s 2 ∣ x) are their conditional distributions given X = x. If, for all s 1 and s 2, G 1(s 1 ∣ x) - G 2(s 2 ∣ x) changes sign at most once from negative to positive as x increases, then the conditional expectation of X given S 1 is greater than the conditional expectation of X given S 2 in the convex order, provided that both conditional expectations are increasing. The stochastic order of the sufficient condition is equivalent to the more stochastically increasing order when S 1 and S 2 have the same marginal distribution and, when S 1 and S 2 are sums of X and independent noises, it is equivalent to the dispersive order of the noises.

scholarly journals A relation between positive dependence of signal and the variability of conditional expectation given signal

2006 ◽  
Vol 43 (4) ◽  
pp. 1181-1185 ◽  
Author(s):  
Toshihide Mizuno
Keyword(s):  
Conditional Expectation ◽  
Marginal Distribution ◽  
Stochastic Order ◽  
Random Variable ◽  
Sufficient Condition ◽  
Conditional Distributions ◽  
Convex Order ◽  
Positive Dependence ◽  
Dispersive Order ◽  
Conditional Expectations

Let S1 and S2 be two signals of a random variable X, where G1(s1 ∣ x) and G2(s2 ∣ x) are their conditional distributions given X = x. If, for all s1 and s2, G1(s1 ∣ x) - G2(s2 ∣ x) changes sign at most once from negative to positive as x increases, then the conditional expectation of X given S1 is greater than the conditional expectation of X given S2 in the convex order, provided that both conditional expectations are increasing. The stochastic order of the sufficient condition is equivalent to the more stochastically increasing order when S1 and S2 have the same marginal distribution and, when S1 and S2 are sums of X and independent noises, it is equivalent to the dispersive order of the noises.

scholarly journals On the continuity of the vector valued and set valued conditional expectations

1989 ◽  
Vol 12 (3) ◽  
pp. 477-486 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Conditional Expectation ◽  
Random Variables ◽  
Random Variable ◽  
Sufficient Condition ◽  
Conditional Expectations ◽  
Vector Valued

In this paper we study the dependence of the vector valued conditional expectation (for both single valued and set valued random variables), on the σ–field and random variable that determine it. So we prove that it is continuous for theL1(X)convergence of the sub–σ–fields and of the random variables. We also present a sufficient condition for theL1(X)–convergence of the sub–σ–fields. Then we extend the work to the set valued conditional expectation using the Kuratowski–Mosco (K–M) convergence and the convergence in the Δ–metric. We also prove a property of the set valued conditional expectation.

A Classification and Closure Properties of Languages for Describing Concurrent System Behaviours

1981 ◽  
Vol 4 (3) ◽  
pp. 531-549 ◽  
Author(s):  
Miklós Szijártó
Keyword(s):  
Formal Languages ◽  
Parallel Program ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Concurrent System ◽  
Closure Properties ◽  
Sequential Program ◽  
Necessary And Sufficient ◽  
Special Case ◽  
Independence Relations

The correspondence between sequential program schemes and formal languages is well known (Blikle and Mazurkiewicz (1972), Engelfriet (1974)). The situation is more complicated in the case of parallel program schemes, and trace languages (Mazurkiewicz (1977)) have been introduced to describe them. We introduce the concept of the closure of a language on a so called independence relation on the alphabet of the language, and formulate several theorems about them and the trace languages. We investigate the closedness properties of Chomsky classes under closure on independence relations, and as a special case we derive a new necessary and sufficient condition for the regularity of the commutative closure of a language.

A Combinatorial Distinction Between Unit Circles and Straight Lines: How Many Coincidences Can they Have?

2009 ◽  
Vol 18 (5) ◽  
pp. 691-705 ◽  
Author(s):  
GYÖRGY ELEKES ◽  
MIKLÓS SIMONOVITS ◽  
ENDRE SZABÓ
Keyword(s):  
Parameter Family ◽  
Sufficient Condition ◽  
Simple Application ◽  
Quadratic Number ◽  
General Sufficient Condition ◽  
Family Of Curves ◽  
Unit Circles ◽  
Triple Points ◽  
Straight Lines ◽  
Special Case

We give a very general sufficient condition for a one-parameter family of curves not to have n members with ‘too many’ (i.e., a near-quadratic number of) triple points of intersections. As a special case, a combinatorial distinction between straight lines and unit circles will be shown. (Actually, this is more than just a simple application; originally this motivated our results.)

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

scholarly journals Inclusions of ternary rings of operators and conditional expectations

2013 ◽  
Vol 155 (3) ◽  
pp. 475-482 ◽  
Author(s):  
PEKKA SALMI ◽  
ADAM SKALSKI
Keyword(s):  
Conditional Expectation ◽  
Ternary Ring ◽  
Conditional Expectations

AbstractIt is shown that if T is a ternary ring of operators (TRO), X is a nondegenerate sub-TRO of T and there exists a contractive idempotent surjective map P: T → X then P has a unique, explicitly described extension to a conditional expectation between the associated linking algebras. A version of the result for W*-TROs is also presented and some applications mentioned.

scholarly journals Curvature Properties of Generalized pp-Wave Metrics

2021 ◽  
Vol 45 (02) ◽  
pp. 237-258
Author(s):  
ABSOS ALI SHAIKH ◽  
TRAN QUOC BINH ◽  
HARADHAN KUNDU
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Sufficient Condition ◽  
Type Condition ◽  
Pure Radiation ◽  
Projective Curvature ◽  
Pp Wave ◽  
Codazzi Type ◽  
Curvature Tensors ◽  
Special Case

The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metrics. It is shown that a generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spacetime is semisymmetric, semisymmetric due to conformal and projective curvature tensors, R-space by Venzi and satisfies the pseudosymmetric type condition P ⋅ P = −13Q(S,P). Again we investigate the sufficient condition for which a generalized pp-wave spacetime turns into pp-wave spacetime, pure radiation spacetime, locally symmetric and recurrent. Finally, it is shown that the energy-momentum tensor of pp-wave spacetime is parallel if and only if it is cyclic parallel. Again the energy momentum tensor is Codazzi type if it is cyclic parallel but the converse is not true as shown by an example. Finally, we make a comparison between the curvature properties of the Robinson-Trautman metric and generalized pp-wave metric.

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