Say I have an SDE as follows:
$$dy_{t}=\theta(\mu-y_{t})dt+J_{t}dN_{t}\sigma dW_{t} \tag{1}$$
where dW is a standard Wiener process and dN is a Poisson process with arrival rate $\lambda$.
How do I then find the mean and the variance? If possible at all?
As the Wiener process is multiplied with the jump I am not sure how to start using stochastic calculus. One idea is to log everything so I can treat each component individually, but am not sure that would work.
Any help is highly appreciated :)
I would like to comment, but I am not among the privileged, so I answer:
Do you think that summing a product involving one (stochastic) differential with another product involving two (stochastic) differentials yields a well-defined expression?