Monte Carlo Methods and Applications
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Discrepancy of van der Corput sequences generated by piecewise linear transformations
Discrepancy of van der Corput sequences constructed by piecewise linear transformations with same slope β > 1 is discussed. If there is no eigenvalues of the Perron-Frobenius operator associated with the dynamical system in |z| > 1/β except 1, the discrepancy equals (logN)k+1/N, where k is the number of the non-Markov endpoints.
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