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'A stochastic process is an adapted process if it is adapted to some filtration' what some filtration. Can I say that astochastic process is an adapted process if (X_t)_{t\geq 0}$est (\mathcal{F}_t)_{t\geq 0}-adapted to a filtration$(\mathcal{F}_t)_{t\geq 0}$Obviously$(X_t)_{t\geq 0}\$ is adapted to the filtration \sigma(X_t, t\geq 0).