Translation:I do not have a ticket.
持っています (motte imasu) and あります (arimasu) are both commonly used to say that a person has/possesses something.
切符があります。(kippu ga arimasu)
A ticket exists. (I have a ticket)
切符を持っています。 (kippu o motte imasu)
I'm carrying a ticket. (I have a ticket)
切符がありません。 (kippu ga arimasen)
The ticket doesn't exist. (I don't have a ticket - either I never bought one, or I've checked where I expected it to be and it's not there)
切符を持っていません。 (kippu o motte imasen)
I'm not carrying a ticket. (I don't have a ticket on me; maybe I left it at home)
Typically on a train you need a ticket to get through the gate to get to the train, and then you need that same ticket to exit the gate.
On a local bus you usually pull a ticket when you get on that says what stop number you got on at, and then show that with the money you pay when you get off.
There are other systems, but I guess to answer your question, in my personal experience "strict".
In countries that use automatic ticket barriers (e.g. Japan and the UK), there are fewer ticket checks onboard the train. This has led to one type of 不正乗車 (fare evasion) called 煙管乗車.
The passenger only buys a ticket between the first two stations and the last two stations. Thus the ticket barriers allow the passenger through even though they have not paid for most of their journey.
However, I strongly recommend you do not try this. It is a criminal offence to fare dodge in Japan. If prosecuted, you would be deported and likely unable to return to Japan.