Yes, the violence in the Israeli-Palestinian conflict has emanated mostly from the Palestinian side. The Palestinians have been very aggressive with Israel regarding its very existence and have used terrorism in every way to try reclaim what they believe is their land. Unfortunately, for Palestine Israel is resolute to say the least and every bit as willing to fight fire with fire. The whole situation is a difficult one as Israel was put there and is just trying to fight for its right to live but Palestine was sort of given the short end of the stick insofar as it did lose land that it had at one time occupied.
Israelis incursions and attacks have always followed a Palestinian strike or attack and Israel tends to use policing and security measures to limit attacks and damage. When Israelis enter Palestianian territory, there is no security checkpoint set up by PLO or Hamas to protect the civilian population from attacks. Thus, the violence tends to be the tactic of the Palestinians.
The Palestinian side has more frequently gone violent in the conflict as far as what I know. Israel is bombed daily from the Palestinian geographic side and this has forced Israel not to fire back, but place missile shields around there territory with help from the United States. Living in the United States however, I might be biased.
America is supporting Israel thanks to the strength of the Israeli lobby in America and the buzzword of anti-semitism that the country likes to throw around, as if Palestinians are not also semitic people. However, the territory belonged to Palestine first, and Israel intensifies the conflict by continuing to push into that territory.