Applications of a formula for the variance function of a stochastic process
The authors consider \(X_t\) solving the following usual one-dimensional stochastic differential equation: \(dX_t= \beta(t,X_t) dB_t+ dN_t\), with \(N_t\) being an adapted square-integrable process with jumps. Itô's formula implies that the variance of \(X_t\) satisfies \[ d\text{ Var}(X_t)= \mathbb{E}[\beta^2(t, X_t)] dt+ \mathbb{E}(\Delta N^2_t)+ 2\text{ Cov}(X_t, d\mathbb{E}(N_t)). \] Comments are done upon some simple particular cases.
scientific article; zbMATH DE number 1310362
scientific article