There is a fine line between sibling discord and sibling bullying, and I often get asked about the latter. I always say, wherever there are more than two people, there is the potential for bullying - and the family home is no different. However, it is the root cause of the bullying that must be addressed in the family home, particularly as family roles are at play in a way that is different from the playground or the boardroom.
Every family has its peacemaker, the funny one, the clown -  the roles which inevitably get assigned, usually unconsciously, throughout childhood. With these roles, and with different personalities, different interests and different genders; come discord, arguments, long silences and often, very fraught atmospheres.
Bullying is different, and we define it in exactly the same way as we do other cases of bullying: the imbalance of power, the repetitive nature, and the absolute intention to cause the other person harm. 
The balance here is very important, because in many sibling relationships, while one causes harm one day and calls names and hurls abuse, the other will readily do the same the next day; and on day three, they are both playing together or going out together as friends.
In sibling bullying, we must look at the continuous element of one being hurt all the time with no balance or fairness.
One aspect we see many, many times is that other child who begins to bully siblings, relatively out of character. This is what I refer to as a 'cause of the home' issue.  On these occasions, it is very common for the child to be experiencing bullying elsewhere, and this is merely a manifestation of the tilted power balance as they try and right their scales and assert themselves in what is their very safe environment.
We also must bear in mind the idea of learned behaviour - is there a family member who believes this behaviour is ok, and therefore it is never addressed or called to task? In these cases, the bullied child will not speak up, as they believe there is a normality to such behaviour.
Bullying in sibling relationships is not okay - equal status must always be retained. This will protect them in other social groups, and will teach them empathy and assertiveness as true life skills; skills they need to foster healthy relationships down the line.
Psychologist & Anti-Bullying Specialist