TY - JOUR
T1 - First passage time statistics of Brownian motion with purely time dependent drift and diffusion
AU - Molini, A.
AU - Talkner, P.
AU - Katul, G. G.
AU - Porporato, Amilcare Michele M.
N1 - Funding Information:
This study was supported, in part, by the National Science Foundation ( NSF EAR 1063717 , NSF-EAR 0628342 , NSF-EAR 0635787 and NSF-ATM-0724088 ), and the Bi-national Agricultural Research and Development (BARD) Fund ( IS-3861-96 ). We wish to thank Adi Bulsara for the helpful suggestions. We also thank Demetris Koutsoyiannis and the other three anonymous reviewers for their helpful suggestions.
PY - 2011/6/1
Y1 - 2011/6/1
N2 - Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such systems requires solving the associated Fokker-Planck equation subject to an absorbing barrier. Transitional probabilities are derived via the method of images, whose applicability to time dependent problems is shown to be limited to state-independent drift and diffusion coefficients that only depend on time and are proportional to each other. First passage time statistics, such as the survival probabilities and first passage time densities are obtained analytically. The analysis includes the study of different functional forms of the time dependent drift and diffusion, including power-law time dependence and different periodic drivers. As a case study of these theoretical results, a stochastic model of water resources availability in snowmelt dominated regions is presented, where both temperature effects and snow-precipitation input are incorporated.
AB - Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such systems requires solving the associated Fokker-Planck equation subject to an absorbing barrier. Transitional probabilities are derived via the method of images, whose applicability to time dependent problems is shown to be limited to state-independent drift and diffusion coefficients that only depend on time and are proportional to each other. First passage time statistics, such as the survival probabilities and first passage time densities are obtained analytically. The analysis includes the study of different functional forms of the time dependent drift and diffusion, including power-law time dependence and different periodic drivers. As a case study of these theoretical results, a stochastic model of water resources availability in snowmelt dominated regions is presented, where both temperature effects and snow-precipitation input are incorporated.
KW - Absorbing barrier
KW - Brownian motion
KW - Snowmelt
KW - Time-dependent drift and diffusion
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U2 - 10.1016/j.physa.2011.01.024
DO - 10.1016/j.physa.2011.01.024
M3 - Article
AN - SCOPUS:79953325284
SN - 0378-4371
VL - 390
SP - 1841
EP - 1852
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 11
ER -