Conditional Convergence

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Related to Conditional Convergence: absolute convergence

conditional convergence

[kən′dish·ən·əl kən′vər·jəns]
The property of a series that is convergent but not absolutely convergent.

Conditional Convergence


a concept of mathematical analysis. The series

is said to be conditionally convergent if it is convergent and the series

(whose terms are the absolute values of the terms of the original series) is divergent.

For example, the series

is conditionally convergent, since the absolute values of its terms form the divergent, harmonic series

If a series is conditionally convergent, then the two series consisting of its positive and negative terms, respectively, are divergent. According to Riemann’s theorem, by an appropriate rearrangement of the terms of a given conditionally convergent series we can obtain a divergent series or a series that has a prescribed sum. If two conditionally convergent series are multiplied term by term, a divergent series may result.

The concept of conditional convergence can be extended to series of vectors, to infinite products, and to improper integrals.

References in periodicals archive ?
When the explanatory variables appropriately describe the humped pattern, one can hardly find the conditional convergence result.
beta]-results, from an absolute convergence between 1991 and 1999 to a conditional convergence over the whole sample period.
Conditional convergence (H2): House price convergence is associated with regional structures.
In this connection, one has to distinguish between absolute and conditional convergence.
Wang did find evidence of conditional convergence in health care expenditures, and in this case the convergence coefficient is significant at the 5 percent level.
The findings of this specification can be seen as evidence of conditional convergence to steady state growth rates that differ across regions.
However, it is statistically significant, in the same periods when the conditional convergence occurs.
Their results provide evidence of significant conditional convergence at a relatively high speed.
This result is well known in the literature and has led many researchers to the conclusion that conditional convergence has been faster than was previously thought.
In "Technological Diffusion, Conditional Convergence, and Economic Growth," (NBER, Working Paper Number 8713), David E.
In the conditional convergence view, growth in output per worker is the result not just of growth in capital per worker and technology, as in the basic neoclassical growth model, but is also conditioned on a host of characteristics of an economy, such as the political system, culture, and the educational system.
1] Although there is no agreement on what determines economic growth, most of the literature points out evidence of conditional convergence.

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