TY - JOUR
T1 - A note on the first-passage problem and VanMarcke's approximation - short communication
AU - Koutsourelakis, Phaedon-Stelios
PY - 2007/1
Y1 - 2007/1
N2 - Given a scalar, stationary, Markov process, this short communication presents a closed-form solution for the first-passage problem for a fixed threshold b. The derivation is based on binary processes and the general formula of Siegert [Siegert AJF. On the first-passage time probability problem. Physical Review 195 1; 81:617-23]. The relation for the probability density function of the first-passage time is identical to the commonly used formula that was derived by VanMarcke [VanMarcke E. On the distribution of the first-passage time for normal stationary random processes. Journal of Applied Mechanics ASME 1975; 42:215-20] for Gaussian processes. The present derivation is based on more general conditions and reveals the criteria for the validity of the approximation. Properties of binary processes are also used to derive a hierarchy of upper bounds for any scalar process. (C) 2006 Elsevier Ltd. All rights reserved.
AB - Given a scalar, stationary, Markov process, this short communication presents a closed-form solution for the first-passage problem for a fixed threshold b. The derivation is based on binary processes and the general formula of Siegert [Siegert AJF. On the first-passage time probability problem. Physical Review 195 1; 81:617-23]. The relation for the probability density function of the first-passage time is identical to the commonly used formula that was derived by VanMarcke [VanMarcke E. On the distribution of the first-passage time for normal stationary random processes. Journal of Applied Mechanics ASME 1975; 42:215-20] for Gaussian processes. The present derivation is based on more general conditions and reveals the criteria for the validity of the approximation. Properties of binary processes are also used to derive a hierarchy of upper bounds for any scalar process. (C) 2006 Elsevier Ltd. All rights reserved.
KW - first-passage problem
KW - binary process
KW - Markov process
UR - https://www.scopus.com/pages/publications/33750326941
U2 - 10.1016/j.probengmech.2006.05.003
DO - 10.1016/j.probengmech.2006.05.003
M3 - Article
SN - 0266-8920
VL - 22
SP - 22
EP - 26
JO - Probabilistic Engineering Mechanics
JF - Probabilistic Engineering Mechanics
IS - 1
ER -