We propose a stochastic phoneme space transformation technique that allows the conversion of conditional source phoneme posterior probabilities (conditioned on the acoustics) into target phoneme posterior probabilities. The source and target phonemes can be in any language and phoneme format such as the International Phonetic Alphabet. The novel technique makes use of a Kullback-Leibler divergence based hidden Markov model and can be applied to non-native and accented speech recognition or used to adapt systems to under-resourced languages. In this paper, and in the context of hybrid HMM/MLP recognizers, we successfully apply the proposed approach to non-native English speech recognition on the HIWIRE dataset.