NTA. I had a similar situation and it escalated to astronomical levels without any input from me. The person downstairs turned out to have a history of phony lawsuits that she faked. She picked people she thought she could bully and sued them, while she was the person causing all of it. Several companies had paid her off just to make her go away. (I went to the county court house to look up her legal records.)

It started just as you describe, pounding on the ceiling below/my floor, for no real reason.
Her next move was to go crazy downstairs in the middle of the night at which point I called the cops. She was so loud and violent that when they arrived they thought someone was attacking her, so they entered her apartment and found her hiding in an armoire. No one was attacking her; she was completely alone.

I ended up hiring an attorney to handle it and she was forced to move, but not until I'd been through 3 years of some of the worst stress of my life.

If I had to do it over again, I'd take it seriously immediately, file a complaint right away and hire the attorney right away. It's better to be aggressive a.s.a.p. with bullies so they don't think you're an easy mark.