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genpark-geometric-brownian-motion-euler-maruyama-skill

mcp
Guvenlik Denetimi
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SUMMARY

Euler-Maruyama and Milstein numerical discretization solvers for Itô Stochastic Differential Equations (SDEs)

README.md

Euler-Maruyama & Milstein SDE Solvers Skill

High-order numerical integration schemes for Itô stochastic differential equations with Brownian increments.

flowchart LR
    S0["Initial Value S_0"] --> Drift["Drift μ S Δt"]
    S0 --> Diff["Diffusion σ S ΔW"]
    S0 --> Milstein["Higher Order Term: 0.5 σ^2 S (ΔW^2 - Δt)"]
    Drift --> Step["Combine Next Step S_{t+1}"]
    Diff --> Step
    Milstein --> Step
    Step --> Trajectory["Complete Discrete Stochastic Trajectory"]

Features

  • 100% Python Standard Library: Box-Muller Gaussian generation.
  • Order 1.0 Strong Convergence: Milstein scheme eliminates discretization bias.
  • MCP Server Ready: Instant stdio simulation for agent forecasting.

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