In my own field of biology, "epigenetics" has a precise definition, specifically variation in DNA methylation, DNA oxidation, or histone acetylation. All three of these can modify gene expression. Differences in DNA methylation can alter histone acetylation and acquired changes in DNA oxidation can influence DNA methylation. It has been recently determined that postnatally aquired modifications of DNA methylations can be inherited on a "permanent" basis (they do not "re-set" during the imprintation stage of development but retain the "acquired" state). In addition to chemical or other "physical" exposures altering DNA methylation and oxidation, in some cases, "behavioral" differences, such as postnatal maternal care, can alter DNA methylation.

Therefore, if a "behavioral" condition, such as maternal care, can alter DNA methylation, postnatally acquired changes in DNA methylation can be inherited and do not automatically re-set, the possibility of inheritence of characteristics due to "behavioral" situations is not implausible, althought it is likely to be rare.