Stochastic Calculus SDE

objective

Simulate and validate SDE dynamics with controlled numerical error and path diagnostics.

workflow

1. define drift and diffusion specifications for target process.
2. implement Euler, Milstein, or higher-order discretization schemes.
3. quantify discretization bias and variance across step sizes.
4. validate path statistics against analytical moments when available.
5. promote simulation settings only after convergence diagnostics pass.

required diagnostics

• strong and weak convergence versus time-step size.
• pathwise moment and autocorrelation consistency checks.
• stability under volatility and drift regime shifts.
• random-seed sensitivity and reproducibility diagnostics.
• tail-path behavior under extreme shocks.