I don’t think it’s prosecution, unless it’s the state doing it.
When there is a criminal prosecution involved, malicious prosecution can be claimed when a complaint to the police that was made without probable cause results in criminal prosecution. There are lots of "privileges" for making police reports, though, so it is much more difficult to make a malicious prosecution case in a criminal setting. Generally, it has to be a false report and you have to have known it was false.
If a false statement results in an arrest, the person making the false statement can also be subject to suit for "false arrest".
False arrest cases are much easier to prove, except against cops. Generally, any arrest that is made with probable cause, as defined in the criminal law, is a false arrest. These happen most often when a store arrests an alleged shoplifter, but any situation when someone is held against their will qualifies as a false arrest.
I used to handle false arrest cases for a large retailer, and I have also done a few plaintiff's cases for people who have been falsely arrested.
Ok, malicious persecution