This paper investigates how the official discourse of race and caste are constructed in response to the Dalits' claims that casteism is racism and caste should be included in the World Conference against Racism, Racial Discrimination, and Xenophobia (WCAR held in Durban in 2001). The research question driving this project probes into discursive strategies and logics, which deny any association of caste with race in the Indian context and the significance of race denial. The paper also questions whether the denial of association of race and caste is indicative of racial Indianization. I argue that in India, race lives through the category of caste as a form of racial Indianization.
We study the concept of quadratic variation of a continuous path along a sequence of partitions and its dependence with respect to the choice of the partition sequence. We define the quadratic roughness of a path along a partition sequence and show that, for Hölder-continuous paths satisfying this roughness condition, the quadratic variation along balanced partitions is invariant with respect to the choice of the partition sequence. Paths of Brownian motion are shown to satisfy this quadratic roughness property almost-surely. Using these results we derive a formulation of Föllmer's pathwise integration along paths with finite quadratic variation which is invariant with respect to the partition sequence.
We investigate the statistical evidence for the use of 'rough' fractional processes with Hurst exponent H < 0.5 for the modeling of volatility of financial assets, using a model-free approach. We introduce a non-parametric method for estimating the roughness of a function based on discrete sample, using the concept of normalized p-th variation along a sequence of partitions. We investigate the finite sample performance of our estimator for measuring the roughness of sample paths of stochastic processes using detailed numerical experiments based on sample paths of fractional Brownian motion and other fractional processes. We then apply this method to estimate the roughness of realized volatility signals based on high-frequency observations. Detailed numerical experiments based on stochastic volatility models show that, even when the instantaneous volatility has diffusive dynamics with the same roughness as Brownian motion, the realized volatility exhibits rough behaviour corresponding to a Hurst exponent significantly smaller than 0.5. Comparison of roughness estimates for realized and instantaneous volatility in fractional volatility models with different values of Hurst exponent shows that, irrespective of the roughness of the spot volatility process, realized volatility always exhibits 'rough' behaviour with an apparent Hurst index H < 0.5. These results suggest that the origin of the roughness observed in realized volatility time-series lies in the microstructure noise rather than the volatility process itself.
We present several constructions of paths and processes with finite quadratic variation along a refining sequence of partitions, extending previous constructions to the non-uniform case. We study in particular the dependence of quadratic variation with respect to the sequence of partitions for these constructions. We identify a class of paths whose quadratic variation along a partition sequence is invariant under coarsening. This class is shown to include typical sample paths of Brownian motion, but also paths which are 1 2 -Hölder continuous. Finally, we show how to extend these constructions to higher dimensions.
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