Brian Hughes, senior vice president for audience analysis at Magna Global, said a study his company conducted when John Oliver filled in for Mr. Stewart in 2013, when he was filming his feature directorial debut, “Rosewater,” offers some encouraging tea leaves for a post-Stewart “Daily Show.”

Ratings for Mr. Oliver’s 31 first-run episodes among adults 18-34 were only slightly below those of Mr. Stewart in the comparable period the previous year.

“With the right host in place, there’s no reason to think that audiences will scatter,” he said. “The brand of ‘The Daily Show’ is still strong.”

Advertisers, however, may take more of a wait-and-see approach. Though Comedy Central does not allow advertisers to cherry-pick an individual show in which to place their commercials, there may be some clients who do business with the network mainly because of Mr. Stewart’s program.