Roman law didn't really have "petty crime," that is actions tried by criminal court but not capital offenses. A "crime" was either crimen, a criminal offense, or else it was not. There were really only a few crimina: murder, treason, etc. Only these were tried by criminal court, with the penalty usually being death or something suitably severe. Any other offense was not crimen but actionable by civil law. The three offenses you mention were not actionable under the same laws, but all three would be some sort of delict (delictum), or offense actionable by lawsuit. Depending on what we mean by vandalism it might be tried under the lex Aquilia, which protected against damage to property. But the lex Aquilia had a relatively narrow definition of damage: property had to be burned (urere), broken (frangere), or "rent," as rumpere is usually translated with respect to this law. The definitions of those verbs expanded over time, but if an action according to the lex Aquilia could not be brought for vandalism, there was always actio in factum, in which case the praetor gave action based on the fact of the case, as there was no civil law that could apply to the particular case. Trespassing was not actually in and of itself liable for suit. Instead trespassing fell under iniuria, damage to reputation. Roman civil law had quite an enormous definition of iniuria, and trespassing cases give a sense of that--technically speaking trespassing on private property was not an offense because of the property, but because trespassing only occurred at houses and property marked with notices, so intruding was ignoring the wishes of the owner, and thus iniuria and an offense against the individual, not against the property. Theft shows the evolution of Romance civil law. As theft involved material damage or loss it was considered delict. As with most delicts the penalty was material (as in all these cases)--thieves paid double the value of the stolen object, or quadruple if the thief was caught red-handed. Quite a severe penalty, but not necessarily one which was really logically just by our standards--arson, in many cases no more serious a crime than many thefts, was a capital offense! Over time theft increasingly was tried as a criminal offense, although I don't know what the penalty was in that case, until by late antiquity civil suits for theft were more or less a thing of the past