Lecture Notes On The Yamada–watanabe Condition For The Pathwise Uniqueness Of Solutions Of Certain Stochastic Differential Equations

In these lecture notes, we discuss the Yamada–Watanabe condition
for the pathwise uniqueness of the solution of certain stochastic differential
equations. This condition is weaker than the usual Lipschitz condition, the
proof is based on Bihari’s inequality. An important application in mathemat-
ical finance is the Cox–Ingersoll–Ross model.