Define stochastic differential equation with an expression

Question

Define the stochastic differential equation with an expression?

Answer 1

Let us assume that we have a random variable y evolving as per to a rather general, a factor stochastic differential equation

dy = A(y, t) dt + B(y, t) dX.

There A and B are arbitrary functions both of y and t. Several common models can be written in such form, as well as the lognormal asset random walk and common spot interest rate models.