I don't think that trend is actually all that well-defined in classical technical analysis (TA), other than being the general direction of a stock, etc.
Trend is actually a rather ambiguous concept (in math, TA, or otherwise), and depends on additional information. Intuitively, I think everyone can agree that trend is quite simply a function with monotone variations. A mathematical definition that captures this is another story. The best definition that I have come across is that the trend in a signal is the contribution to it that is slowly varying in comparison to its fluctuations. In this case, the trend can be calculated by filtering out the high-frequency intrinsic mode functions.