It depends on what species you have in mind. "Ghost shrimp" is a truly vague term applied to a broad range of species - ranging from freshwater to estuarine-brackish and pure marine conditions - of the
Palaemonidae. A more specific specification of taxonomy would be helpful, as breeding conditions are analogously myriad (the vast majority of
true freshwater ghost shrimp (
Palaemonetes) breed and live in freshwater; some "freshwater" ghost shrimp are actually brackish to marine (some species have truly broad salinity tolerance), as
Palaemonetes pugio, but will never thrive in full freshwater, and will reproduce only under optimum salinity (that is, at least somewhat salty water). Compounding the matter is the fact that there are true clades of outwardly similar, yet fully marine "ghost shrimp" (sometimes "glass shrimp", "grass shrimp", or, more broadly, "prawns") -
Palaemon and associated genera, as well as some
Macrobrachium sp. ("long-arm shrimp" or "freshwater prawns") that can tolerate salty conditions. Many unrelated crustaceans are termed "ghost shrimp" as well: callianasids - not shrimp at all, but actually allied with hermit crabs and burrow-dwellers in muddy substrate, and some free-living commensal shrimp, as certain
Stenopus, closely related to "banded coral shrimp".
Look to the following illustrated key:
Palaemonetes sp.: freshwater (will not last long, if acclimated, in marine conditions & generally breeds in freshwater): color ranges from nearly fully transparent (as per the titular denomination), excepting certain internal organs, to slightly gold- or red-tinged.
Another freshwater (sometimes marginally brackish)
P. antennarius, of the Mediterranean rim:
Crangon: a saltwater denizen; no special salinity changes required for breeding.
What is probably
Palaemon (or quite possibly even
Macrobrachium) sp., captured in brackish-marine conditions.
Palaemon sp. - the marine 'feeder' "ghost shrimp" you most likely are referrring to; full saltwater - is capable of being bred in captivity (planktonic larvae are quickly consumed by other aquarium inhabitants, though).
A beautiful saltwater
Palaemon sp.
Yes, they can be bred in captivity: see
http://yamada.cside.com/small/lives/l99032.html for some excellent pictures of eggs, zoea, and adults (scroll down).