You are in a stat-arb team modeling a pairs trading spread using an Ornstein-Uhlenbeck process: $dx_t = \kappa(\theta - x_t)dt + \sigma dW_t$. The mean $\theta=0$ and reversion speed $\kappa=2$. If the current spread is 10, what is the expected spread in half a year ($t=0.5$)? What does the variance of the spread converge to as time goes to infinity?

你在统计套利团队，用 Ornstein-Uhlenbeck (OU) 过程给配对交易的价差建模：$dx_t = \kappa(\theta - x_t)dt + \sigma dW_t$。均值 $\theta=0$，回归速度 $\kappa=2$。如果当前价差是 10，半个月（$t=0.5$）后你预期的价差是多少？随着时间趋于无穷，价差的方差收敛到多少？