Suppose $X$ is an Ito process defined by $ dX = adt + b_tdB$ and $X_0 = 0$ where $B$ is a Brownian motion. Ito process consists of two parts: one is deterministic and the other is random. Is the expectation only decided by the deterministic part, i.e. $E(X_t)=at$ ? And why? More generally, if $ dX = a_tdt + b_tdB$, is $E(X_t) = \int_0^ta_sds$ ?
2026-03-26 03:18:46.1774495126
Expectation of Ito Process
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