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This paper concerns the H ∞ filtering of Markov jump nonlinear systems with general uncertain transition probabilities allowed to be uncertain and unknown. Attention is focused on the construction of an extended filter such that the filtering error system is stochastically stable with a prescribed H ∞ performance requirement. Effective strategies are developed to deal with nonlinearities induced by uncertain and unknown transition probabilities and system nonlinearities, which is also the main contribution of this work. Based on these strategies, sufficient conditions to render the filtering error systems stochastic stable with the prescribed H ∞ performance are established in the framework of linear matrix inequalities. The validity of the proposed filtering scheme is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]