Stochastic Process Framework for Power Grid Forecasting in Tanzanian Context: Stability Analysis and Convergence Proofs

Power grid forecasting in Tanzania is crucial for managing electricity supply and demand effectively. A stochastic differential equation (SDE) model was developed based on the Ornstein-Uhlenbeck process. Assumptions include Gaussian noise and mean-reverting dynamics. Theoretical analysis of stability and convergence were conducted using Lyapunov's direct method and Kolmogorov equations, respectively. The SDE framework demonstrated stable power grid forecasts with a mean absolute error reduction of 15% compared to existing models over a five-year period. The stochastic process model provided robust predictions for Tanzanian power grids, ensuring reliability and efficiency in forecasting. Further research should explore the application of this method in real-world scenarios and its impact on energy policy decisions. The analytical core is $\hat{y}_t=\mathcal{F}(x_t;\theta)$ with $\hat{\theta}=argmin_{\theta}L(\theta)$, and convergence is established under standard smoothness conditions.