$$
\begin{array}{l} \boldsymbol {x} _ {t} = e ^ {\int_ {s} ^ {t} \left(\frac {\mathrm {d} \log \alpha_ {u}}{\mathrm {d} u} - \left(1 + \tau^ {2} (u)\right) \frac {\mathrm {d} \lambda_ {u}}{\mathrm {d} u}\right) \mathrm {d} u} \boldsymbol {x} _ {s} \\ + \int_ {s} ^ {t} e ^ {- \int_ {t} ^ {u} \left(\frac {\mathrm {d} \log \alpha_ {v}}{\mathrm {d} v} - \left(1 + \tau^ {2} (v)\right) \frac {\mathrm {d} \lambda_ {v}}{\mathrm {d} v}\right) \mathrm {d} v} \left[ \left(1 + \tau^ {2} (u)\right) \alpha_ {u} \boldsymbol {x} _ {\boldsymbol {\theta}} (\boldsymbol {x} _ {u}, u) \frac {\mathrm {d} \lambda_ {u}}{\mathrm {d} u} \right] \mathrm {d} u \\ + \int_ {s} ^ {t} e ^ {- \int_ {t} ^ {u} \left(\frac {\mathrm {d} \log \alpha_ {u}}{\mathrm {d} v} - \left(1 + \tau^ {2} (v)\right) \frac {\mathrm {d} \lambda_ {v}}{\mathrm {d} v}\right) \mathrm {d} v} \tau (u) \sigma_ {u} \sqrt {- 2 \frac {\mathrm {d} \lambda_ {u}}{\mathrm {d} u}} \mathrm {d} \bar {w} _ {u}. \\ = e ^ {\int_ {s} ^ {t} \left(\frac {\mathrm {d} \log \sigma_ {u}}{\mathrm {d} u} - \tau^ {2} (u) \frac {\mathrm {d} \lambda_ {u}}{\mathrm {d} u}\right) \mathrm {d} u} \boldsymbol {x} _ {s} \\ + \int_ {s} ^ {t} e ^ {- \int_ {t} ^ {u} \left(\frac {\mathrm {d} \log \sigma_ {v}}{\mathrm {d} v} - \tau^ {2} (v) \frac {\mathrm {d} \lambda_ {v}}{\mathrm {d} v}\right) \mathrm {d} v} \left[ \left(1 + \tau^ {2} (u)\right) \alpha_ {u} \boldsymbol {x} _ {\boldsymbol {\theta}} (\boldsymbol {x} _ {u}, u) \frac {\mathrm {d} \lambda_ {u}}{\mathrm {d} u} \right] \mathrm {d} u \\ + \int_ {s} ^ {t} e ^ {- \int_ {t} ^ {u} \left(\frac {\mathrm {d} \log \sigma_ {v}}{\mathrm {d} v} - \tau^ {2} (v) \frac {\mathrm {d} \lambda_ {v}}{\mathrm {d} v}\right) \mathrm {d} v} \tau (u) \sigma_ {u} \sqrt {- 2 \frac {\mathrm {d} \lambda_ {u}}{\mathrm {d} u}} \mathrm {d} \bar {w} _ {u} \\ = \frac {\sigma_ {t}}{\sigma_ {s}} e ^ {- \int_ {s} ^ {t} \tau^ {2} (u) \frac {\mathrm {d} \lambda_ {u}}{\mathrm {d} u} \mathrm {d} u} \boldsymbol {x} _ {s} \tag {31} \\ + \int_ {s} ^ {t} \frac {\sigma_ {t}}{\sigma_ {u}} e ^ {- \int_ {u} ^ {t} \tau^ {2} (v) \frac {\mathrm {d} \lambda_ {u}}{\mathrm {d} v} \mathrm {d} v} \left[ \left(1 + \tau^ {2} (u)\right) \alpha_ {u} \boldsymbol {x} _ {\boldsymbol {\theta}} (\boldsymbol {x} _ {u}, u) \frac {\mathrm {d} \lambda_ {u}}{\mathrm {d} u} \right] \mathrm {d} u \\ + \int_ {s} ^ {t} \frac {\sigma_ {t}}{\sigma_ {u}} e ^ {- \int_ {u} ^ {t} \tau^ {2} (v) \frac {\mathrm {d} \lambda_ {v}}{\mathrm {d} v} \mathrm {d} v} \tau (u) \sigma_ {u} \sqrt {- 2 \frac {\mathrm {d} \lambda_ {u}}{\mathrm {d} u}} \mathrm {d} \bar {w} _ {u}. \\ = \frac {\sigma_ {t}}{\sigma_ {s}} e ^ {- \int_ {\lambda_ {s}} ^ {\lambda_ {t}} \tau^ {2} (\tilde {\lambda}) \mathrm {d} \tilde {\lambda}} \boldsymbol {x} _ {s} \\ + \sigma_ {t} \int_ {\lambda_ {s}} ^ {\lambda_ {t}} e ^ {- \int_ {\lambda} ^ {\lambda_ {t}} \tau^ {2} (\tilde {\lambda}) \mathrm {d} \tilde {\lambda}} (1 + \tau^ {2} (\lambda)) e ^ {\lambda} \boldsymbol {x} _ {\boldsymbol {\theta}} (\boldsymbol {x} _ {\lambda}, \lambda) \mathrm {d} \lambda \\ + \sigma_ {t} \int_ {s} ^ {t} e ^ {- \int_ {u} ^ {t} \tau^ {2} (v) \frac {\mathrm {d} \lambda_ {v}}{\mathrm {d} v} \mathrm {d} v} \tau (u) \sqrt {- 2 \frac {\mathrm {d} \lambda_ {u}}{\mathrm {d} u}} \mathrm {d} \bar {w} _ {u}. \\ \end{array}
$$