(adsbygoogle = window.adsbygoogle || []).push({}); Deriving Probability Density Functions from Partial Differential Equations???

Hiyas,

I have been told that it is quite normal to get PDFs (Probability Density Functions) from PDEs (Partial Differential Equations). That in PDEs that the function can be a PDF and you can get this by solving the PDE.

Nobody has actually shown me how this is done. I have my doubts because I have learned that Probability Theory is not mixed with PDEs directly this way. That there are other types of mathematics called Stochastic Partial Differential Equations or Stochastic Differential Equations that do something similar.

I was taught to believe that PDFs are found by "reinterpreting" the PDE by approaching it with Probability Theory and looking at from a new way and creating new Probability Mathematics to deal with the PDE.

However others are insisting that I don't start by approaching it with Probability Theory. That I actually just solve PDEs to get PDFs and that I can also get PDFs from PDEs.

Another thing is they are using the term Probability Distribution Function and not Probability Density Function but I think they are claiming them to be the same thing.

Can anyone give me their thoughts on this.

Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Deriving Probability Density Functions from Partial Differential Equations?

**Physics Forums | Science Articles, Homework Help, Discussion**