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A closed-form expression is obtained for the conditional probability distribution of ∫t 0 R 2 s ds given R t, where (R s, s ≧ 0) is a Bessel process of dimension δ > 0 started from 0, in terms of parabolic cylinder functions. This is done by inverting the following Laplace transform also known as the generalized Lévy’s stochastic area formula: [exp(λ220tRs2ds)|Rt=a]=(λtsinh(λt))δ/2exp(a22t(λtcoth(λt)1)). We also examine the joint distribution of (R 2 t, ∫t 0 R 2 s ds.

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-related factors over the last 40 years. Shown in Table 1 , specific government interventions and structural events, such as the 1997–1998 financial, IMF-related crisis, can facilitate regional innovation system generation. There have been multiple attempts to

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from IMF ( 2009 ). GDP: Percentage of World's GDP in current US$ in 2008, IMF ( 2009 ). N: Number of universities from which system averages are computed. Score: Normalized score on the one dimensional ARWU scale (value of the first principal component

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, the larger its scientific knowledge output. The source of population size (in million units) is also the IMF database. Countries considered too small (less than 1,000,000 inhabitants) were excluded from the analysis, as well as those for which data

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: GdP: Percentage of World's GDP in current US$, IMF( 2009 ). NoU: Number of averaged universities to produce the system scores. AlU: Averaged score of a university system on the indicator Alumni. AwD: Averaged score on the indicator Award. HiCi

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related Taiwan and Malaysia data were extracted from MOSTI ( 2008 ) and IMF ( 2009 ), respectively. This dataset includes information on GDP and R&D investment. The statistics for the input and output indicators were also taken from this dataset. The

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's non-parametric correlation test. Publication patterns were also compared with the Human Development Index per country (HDI, data for 2010, UNDP 2010 ) and Gross Domestic Product derived from purchasing power parity (GDP, data for 2010, IMF

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GDP data for the period 1981–2007. Nominal GDP data in US dollars were taken from the International Monetary Fund's (IMF) World Economic Outlook Database (2009/4). Publication data were taken from the National Science Indicators (NSI) database compiled

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Scientometrics
Authors: Mauricio Uriona-Maldonado, Raimundo N. M. dos Santos, and Gregorio Varvakis

Economic Cooperation and Development (OECD), the United Nations Conference on Trade and Development (UNCTAD), the World Bank and the International Monetary Fund (IMF) use the approach to inform policy-making and to conduct research on regional and national

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.000731 D IMF Staff Papers 0.000940 0.000522 0.000482 0.000644 D

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