Analyze Diffusion Dynamics

Characterize the behavior of diffusion processes by specifying their stochastic differential equations, deriving the corresponding Fokker-Planck equation, computing first-passage time distributions analytically or numerically, performing parameter sensitivity analysis, and validating analytical results against Monte Carlo simulation.

When to Use

• Deriving the probability density evolution of a continuous-time diffusion process
• Computing mean first-passage times or full first-passage time distributions for bounded diffusion
• Analyzing how drift, diffusion coefficient, and boundary parameters affect process behavior
• Validating closed-form solutions against stochastic simulation
• Building intuition for the dynamics underlying drift-diffusion models or generative diffusion processes

Inputs