Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise

• The first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input.
• The problem is handled step-by-step accounting for the Markov properties.
• The final formulation consists just of a sequence of matrix–vector multiplications giving the reliability density function in time.
• The procedure works for linear and non-linear systems, for normal and Poissonian noise.
• Results are reported for linear and nonlinear systems and compared with those obtained by Monte Carlo simulation.

In this paper the first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input. The problem is handled step-by-step accounting for the Markov properties of the response process and then by Chapman–Kolmogorov equation. The final formulation consists just of a sequence of matrix–vector multiplications giving the reliability density function at any time instant. Comparison with Monte Carlo simulation reveals the excellent accuracy of the proposed method.