I am a stochastic analysis student and am particularly interested in stochastic differential equations. What always struck me as odd is how little PDE (or even ODE for that matter) seems to have anything to do with SDE. My reasons for thinking so are the following.
- I've read on SDE many times and never encountered a single mention of PDE/ODE
- My master's programme offers almost nothing on PDE.
- Searching for both tags on math.SE
- I encountered PDE literally only once in my life, while dealing with continuous time Markov processes.
Recently, I've been drifting towards biology and started encountering PDEs more and more. This is not surprising, as they are arguably much more useful in that area than SDEs. It makes me wonder, however, whether I should perhaps devote time to ODE/PDE. This leads me to the following questions:
- Are PDE really so rarely relevant when it comes to SDE? Or possibly stochastic analysis in general?
- What could a stochastics student take away from studying ODE/PDE? What areas should he/she focus on (if any)? (e.g. very basics of ODE, at least)
- Since I am going into biology and thus might regret not knowing more PDE, how much sense would it make to make them a serious (secondary) area of study? Could sometimes PDE and SDE be seen as two approaches to the same problem, or be somehow analogous? Could they compliment each other, or would I just be doomed to be studying two mostly unrelated fields?