Is it possible to become a professor in a field where you don't have a PhD degree? I am a economics major student who will be applying for PhD programmes pretty soon. I am quite interested in economics, but I find myself even more interested things related to probability theory, such as stochastic processes. And if I ever get into a econ PhD programme, I'm pretty sure that I should be looking for co-advising from the math/statistics department if allowed. 

So I am curious about what happens in academia if you ever find yourself more interested in a topic that you don't have a degree on. If you can write some good papers during your PhD, can you find good career opportunities in that field in academia even if you did not start out as a "professional" scholar in that field? 

Any idea would be very much appreciated!!
Yes, it is possible to cross over between different fields following the PhD-level studies. However, in general, this tends to be more applicable to "interdisciplinary" fields that can fall into multiple disciplines. For instance, the engineering department I studied at hired people with PhD's in applied mathematics and physics, because their research fields—in fluid mechanics and interfacial science, respectively—meshed well with the research interests of the department.

To give a counterexample, however, it will be much harder to make the case for a high-energy physics person to move into another discipline, just because it is so strongly identified with physics.

Thus, if you have a PhD in a field such as mathematical economics or econometrics, it will be a lot easier to make the lateral shift. However, if you're in a more "traditional" subfield, that move becomes much more challenging.