eal-World Application: Stock Prices (Finance) Let’s say you want to model the price of a stock, like Apple or Tesla. Denote 𝑋 𝑡 X t ​ : the price of the stock at time 𝑡 t. The price isn’t fixed—it’s affected by random factors (news, investor behavior, etc). So, we model 𝑋 𝑡 X t ​ as a random variable, and the full set { 𝑋 𝑡 , 𝑡 ≥ 0 } {X t ​ ,t≥0} as a stochastic process. In this case: We might use Brownian motion or Geometric Brownian motion as mathematical models of the process. These models help in pricing options, risk management, and algorithmic trading.