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

• Required: SDE specification (drift function, diffusion coefficient, domain/boundaries)
• Required: Parameter values or ranges for the drift and diffusion functions
• Required: Boundary conditions (absorbing, reflecting, or mixed)
• Optional: Time horizon for transient analysis (default: auto-detect from dynamics)
• Optional: Spatial discretization resolution for numerical PDE solvers (default: dx=0.001)