I am currently using the FinRL library to try to automate Trading using Reinforcement Learning. However, I wanted to understand how FinRL simulates the stock market using historical data. I read here that they "simulate live stock markets with real market data according to the principle of time-driven simulation", but I could not figure out what is meant by time-driven simulation.
Unrelated to FinRL I read here that you could do it with geometric Brownian motion like this: Assume you have historical stock data $S_0, \dots, S_N$. Then we can calculate the log returns $$ r_1 = \log\left(\frac{S_1}{S_0}\right), \dots, \log\left(\frac{S_N}{S_{N-1}}\right) $$ Then we can estimate the empirical mean and standard deviation of the log returns $\hat \mu$ and $\hat \sigma$ and simulate a brownian motion $W_t$ and then simulate the stock market using $$ S_t = S_0 e^{(\hat \mu - \frac{\hat\sigma^2}{2})t + \hat \sigma W_t} $$ Does anyone know if FinRL actually simulates the stock market like this? If not, what are some other (common) ways to realistically simulate the stock market using historical data? Maybe use a time series model with estimated parameters from the given historical data (maybe some references?)?