§ IDefinition
One of the four cardinal Stoic TERMπάθη (passions). In the Stoic matrix of passions along two axes ("good/evil" × "present/future"), ἐπιθυμία occupies the slot apparent good in the future: the soul judges "this (external) thing is a good that I ought to acquire" — and from this false evaluative assent arises an "irrational impulse" (ἄλογος ὄρεξις) toward the object. Chrysippus' formula (Stob. Ecl. II 90 W): ἐπιθυμία ἐστὶν ἄλογος ὄρεξις — "desire is an irrational impulse."
For the Stoics every form of obsessive wanting is a species of ἐπιθυμία: ἔρως (erotic love), σπάνις (longing for what one lacks), φιλοπλουτία (love of wealth), φιλοδοξία (love of glory), ὀργή (anger — "the desire for revenge"!), and so on. This typological move is principled: ἐπιθυμία for the Stoics is the generic class of partial directedness toward the not-yet-attained, not a "lower" wanting opposed to a "higher" one (as in Plato's Resp. IV).
The eupatheia-correlate (the sage's correct disposition occupying the same slot) is βούλησις — "rational wishing" — directed at what is truly good (virtue and what accords with it).
§ IISource
SVF III 391–442 (the doctrine of the passions); specifically on ἐπιθυμία: III 394–397, 412; DL VII 113; Stob. Ecl. II 88–93 W; Cic. Tusc. IV 11–14, 19–22; LS 65. In Marcus: Med. 2.10; 2.16; 5.28; 9.7; 11.20.
§ IIINotes
In 02-10 ἐπιθυμία is opposed to TERMθυμός within the Theophrastean typology: offences born of desire are graver than offences born of anger. The Stoic nuance: strictly speaking, in Stoic doctrine even θυμός (anger) is itself a species of ἐπιθυμία (as is ὀργή — the desire to punish). Marcus here operates within the Peripatetic frame, in which ἐπιθυμία and θυμός are parallel categories. The Theophrastean argument turns on the "initiative" of the offence: desire issues from within, whereas anger is reactive (forced by an antecedent pain). This gives Marcus an ethical criterion of relative gravity: a voluntarily chosen offence is graver than a reactive one. See TERMhedone — the state under whose sway the ἐπιθυμία-offence is committed (ὑφ' ἡδονῆς ἡττώμενος).