The upper and lower quantization coefficient for Markov‐type measures

We study the asymptotic quantization error for Markov‐type measures μ on a class of ratio‐specified graph directed fractals E . Assuming a separation condition for E , we show that the quantization dimension for μ of order r exists and determine its exact value in terms of spectral radius of a related matrix. We prove that the ‐dimensional lower quantization coefficient for μ is always positive. Moreover, we establish a necessary and sufficient condition for the ‐dimensional upper quantization coefficient for μ to be finite.