Let $\lbrace X_t \rbrace_{t\geq 0}$ , $\lbrace Y_t\rbrace_{t\geq 0}$ be stochastic processes on $(\Omega, \mathcal{F}, P)$ . $\lbrace X_t \rbrace_{t\geq 0}$ is a modification of $\lbrace Y_t\rbrace_{t\geq 0}$ if $$P[\{\omega:X_t(\omega)=Y_t(\omega)\}]=1$$ for all $t \in [0, \infty).$

Bibliography

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Bernt Øksendal. Stochastic Differential Equations, (An Introduction with Applications), 5th ed Springer 1998.