English often uses helping verbs to aid in designating verb tense (e.g., will go) or to specify a change in voice (e.g., he was led). While Greek usually indicates tense by prefixes and suffixes to the verb, it also uses ei]mi< + participle to indicate a single verbal idea. ei]mi< + participle is called a periphrastic construction.
Periphrastic constructions are formed with present and perfect participle forms. The ei]mi< may be of any tense. When using the present participle, the tense of the ei]mi< form matches the tense with which it is translated. With the perfect participle, the perfect tense uses the present forms of ei]mi<, and the pluperfect tense uses the imperfect forms.
Gal. 1:23 (Imperfect ei]mi< + present ptc.)
But only, they kept hearing that
Mat. 16:19 (Future ei]mi< + perfect ptc.)
will have been bound in heaven (Hewitt, New Testament Greek, 151f.)
Translate the periphrastic form as the normal tense of the verb. While there may be an emphasis on continuous aspect of the verb, the context will determine if the aspect is the actual focus of the construction. Normally, however, translate periphrastic constructions like the regular verb tense (Mounce, Basics, 277). Note the absence of the aorist participle. Some think that it is because of the durative/continuous/process force reflected in the periphrastic. Porter observes that no elements may be inserted between the auxiliary verb (ei]mi<) and the participle except those which complete or modify the participle (Porter, Idioms, 45).
A genitive absolute links a participle and a noun or pronoun in the genitive case and is only loosely connected to the rest of the sentence. The subject of the sentence is not the subject of this participial construction. The construction Participle (gen.) + noun/pronoun (gen.) is called “absolute” from the Latin “absolutus,” which means “separated” (Mounce, Basics, 275). The genitive noun is often taken as the subject of the participle. This construction is used when there is a pronounced shift in characters in the narrative (“he/she” to a different “they” etc.)(Stevens, 300).