1. A speech processing device comprising: an analysis unit that is configured to output a feature amount by performing speech detection/analysis of input speech; and a speech recognition unit that is configured to output a recognition result by performing speech recognition based on the feature amount, wherein: said speech recognition unit comprises a phrase determination unit that is configured to determine a phrase boundary based on comparison between a hypothetical word group generated by the speech recognition and a word representing phrase boundary set in advance, said speech recognition unit is configured to output the recognition result for each phrase up to the phrase boundary determined by said phrase determination unit, said phrase determination unit is configured to stand by until an occupation ratio of a number of the words representing the phrase boundaries in the hypothetical word group generated by the speech recognition unit to a number of all the words of the hypothetical word group exceeds a set threshold, and said phrase determination unit is configured to determine the phrase boundary based on a likelihood of the word representing the phrase boundary in the hypothetical word group when the occupation ratio exceeds the set threshold.