Random Walk — First Passage Time

1D Brownian motion hitting an absorbing barrier — distribution of τ

Barrier L60

Drift μ0.00

σ (volatility)1.0

Walkers/batch10

Mean τ: —

Theory (μ=0): —

Median τ: —

Max steps: —

Theory: E[τ] = L²/σ² (μ=0). Lévy arcsine law governs the distribution. For μ>0: E[τ] = L/μ. Inverse Gaussian distribution for FPT.