TY - JOUR
T1 - Stochastic Ornstein-Uhlenbeck capacitors
AU - Eliazar, Iddo
AU - Klafter, Joseph
N1 - Publisher Copyright:
© 2005 Springer Science+Business Media, Inc.
PY - 2005
Y1 - 2005
N2 - We introduce and study a class of random capacitor systems which are both charged and discharged stochastically. A capacitor is ‘fed’ by a random inflow with stationary and independent increments. Discharging occurs according to a Markovian rate which is linear in the capacitor’s level. The resulting capacitor dynamics are Markovian, stochastically cyclic, and regenerative. We coin these systems “Lévy-charged Ornstein-Uhlenbeck capacitors”. Various random quantities associated with these systems are analyzed, including: the time-todischarge; the duration of the charging cycle; the trajectory and the peak height of the capacitor level during a charging cycle; and, the capacitor’s stationary equilibrium level. Furthermore, we show that there are sharp distinctions between these capacitor systems and corresponding ‘standard’ Lévy-driven Ornstein-Uhlenbeck systems.
AB - We introduce and study a class of random capacitor systems which are both charged and discharged stochastically. A capacitor is ‘fed’ by a random inflow with stationary and independent increments. Discharging occurs according to a Markovian rate which is linear in the capacitor’s level. The resulting capacitor dynamics are Markovian, stochastically cyclic, and regenerative. We coin these systems “Lévy-charged Ornstein-Uhlenbeck capacitors”. Various random quantities associated with these systems are analyzed, including: the time-todischarge; the duration of the charging cycle; the trajectory and the peak height of the capacitor level during a charging cycle; and, the capacitor’s stationary equilibrium level. Furthermore, we show that there are sharp distinctions between these capacitor systems and corresponding ‘standard’ Lévy-driven Ornstein-Uhlenbeck systems.
KW - Lévy inflow
KW - Ornstein-Uhlenbeck dynamics
KW - Stochastic capacitors
UR - http://www.scopus.com/inward/record.url?scp=34247631441&partnerID=8YFLogxK
U2 - 10.1007/s10955-004-8782-8
DO - 10.1007/s10955-004-8782-8
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AN - SCOPUS:34247631441
SN - 0022-4715
VL - 118
SP - 177
EP - 198
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 1-2
ER -