= Itô process
{c}
{title2=$X_t=X_0+\int_0^t b_sds+\int_0^t\sigma_s dW_s$}
An Itô process is a continuous <semimartingale> expressible as the displayed sum, with adapted coefficients locally integrable for the time integral and locally square integrable for the <Itô integral>. The coefficients may depend on the whole past; an <Itô diffusion> usually specifies them as functions of the current state and time. A continuously differentiable deterministic process is an Itô process with zero Brownian coefficient. The <Itô formula> and <Itô product rule> apply to these processes.
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