Looks more like windburn, or cold injury whenever the leaves were smaller, maybe even bud-sized. Also possibly a spray injury.
kevin

it's indoors and away from the windows. The weather was warm when this photo was taken.

Any chance that it could be excessive nutrition? I believe that some plants show browning at the leaf tips when they get too much fertilizer, though I don't know what the situation is specifically for jasmine.

Distinct possibility. I did overfertilize, and noticed some burning, but haven't fertelized in a long time since. I figure the excess has long since leached out, but it still going on a long slow decline. No matter, it was getting too big and thirsty, and the flowers smelled funny to me.

Have you checked the plant's roots recently? I root-pruned my sambac this summer and was shocked to find out how much better it did afterwards.

root prune? not familiar; I'll have to look that up. I suppose it could be rotting down there, although I don't water it enoughto begin with.

My plant just had so many roots that water wasn't draining well, with the probable result that it wasn't getting appropriate amounts of water or nutrients. I just used a bread knife to chop off a lot of the rootball (at least half), and then put it back in the pot with fresh potting mix. It grew new shoots within a few days.