CV's and résumés—when am I an expert?

I'm never quite certain when it's appropriate to add a particular skill or specialty to my CV or Linkedin profile. For example, I've been working on stochastic differential equations lately and can now simulate them for a few special cases. Does this mean that I can honestly state that I have experience with stochastic differential equations on my CV?

Logically speaking, I do have some experience, so the answer to the above question is "yes." However, I still have some reservations since I'm only familiar with such a small portion of the subject that I feel it would be dishonest to claim them as a job skill. The issue, then, is whether I possess a degree of competency with the subject that allows me to ethically place it as a specialty area on my CV.

I can think of a few ways to justify doing so. The first—and I know that this is a fallacious argument—is that many people add skill sets to their résumés or CV's that they are not entirely proficient in. If I am to compete against others for a job, then I should play by the same rules. Though this argument is logically flawed and morally questionable, it is simply one rule of the game.

Second, and much more sound, is that some areas of expertise, like stochastic differential equations, contain so much material that few people can claim that they are intimate with all of this knowledge. I could argue that my brief exposure to them has provided me with the resources to respond appropriately to a problem, i.e. I am now able to research its solution in a collection of references that I've already compiled. Without the prior experience, I would not have these resources and so I'm justified in claiming this subject as a skill. To put it another way, it's not so much the content of the subject matter but rather the ability to find appropriate solutions within its toolbox that counts. Of course, this detracts from individuals who really are experts in the subject matter, so this argument is morally questionable as well.

One final solution is simply to sort my skills in degrees of competency, such as expert, proficient, and familiar. This lessens any moral ambiguities because I may still add skills that I have limited experience with. On my CV, I have taken this approach and feel quite satisfied with it.