# Conditional Convergence

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Related to Conditional Convergence: absolute convergence

## conditional convergence

[kən′dish·ən·əl kən′vər·jəns]
(mathematics)
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.

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References in periodicals archive ?
The regression results confirm conditional convergence as the coefficient of the regression slope is negative, [[alpha].
0] may be interpreted as a factor of conditional convergence and expresses the catch-up effect towards the steady state.
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.
The concept of conditional convergence corresponds to the concept of [sigma]-convergence, which occurs when the variance of indicator [y.
In this connection, one has to distinguish between absolute and conditional convergence.
When testing conditional convergence, the objective was to estimate the following equation:
Alternate definitions of conditional sigma convergence are proposed, following the distinction used by Barro and Sala-I-Martin (1991) to differentiate conditional [beta] and non 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.
3 Further, we included one period lagged values of natural log of real GDP per capita [LGRGDP (-1)] in pooled regression models to check the conditional convergence of output growth for the countries included in the sample.
Differently, testing for the conditional convergence hypothesis by the panel data approach suggests support for of conditional b-convergence over the periods 1979-1988, 1998-2007 and the entire period, as shown in Table 7.
Unconditional convergence implies that the countries/regions converge to a common steady state while the conditional convergence implies that the countries/regions converge to their own steady state.

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