I am looking for a stochastic differential equation of the form $$X_i = \sum_{j=1}^m \int a_{ij}(X) \, dZ_j + N_i$$
that models something more or less important, something with practical use, where $X=(X_1, \ldots, X_n)$ is an $n$-dimensional cadlag adapted stochastic process, $Z_j$ are semimartingales, $N$ a cadlag adapted $n$-dimensional process such that $N(0)=X(0)$ and $a_{ij}$ are at least locally Lipschitz functions that map cadlag adapted processes on $L^1(Z_j)$ processes.
We can prove existence and uniqueness of solution $X$ in the space of cadlag adapted processes (up to evanescence). I am wondering if those equations can model something that has practical use, in any kind of subject (biology, finance, aerospace, climate...)