Would that include recessive genes as well?
What particular stochastic process is used to model it?
For example, Markovian would be memoryless.
Dominant and recessive (and partially dominant, etc.) are all passed on by the same mechanism. Of course, having such a gene may change the survival probabilities. There're several books about the subject, but I don't remember the names. GOOGLE may be of help. The subject is "population genetics."