= Solution
A <strong solution of a stochastic differential equation> is adapted to the completed filtration of a prescribed Brownian motion $B$ on a prescribed probability space and satisfies
$$
X_t=X_0+\int_0^tb(X_s)\,ds+\int_0^t\sigma(X_s)\,dB_s
$$
almost surely. A <weak solution of a stochastic differential equation> may choose the filtered probability space, Brownian motion, and adapted process as part of the solution; only the displayed integral equation and the prescribed initial law are required.
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