Diffusion local time storage

Stochastic Processes and their Applications

Volumn 114, Issue 2, 2004, Pages 211-229

  Kozlova, M ^a   Salminen, P ^a  

^a ÅBO AKADEMI UNIVERSITY   (Finland)

Author keywords

Brownian motion with drift; Busy periods; Diffusion processes; Idle periods; Palm probability; Spectrally positive L vy processes

Indexed keywords

BROWNIAN MOVEMENT; GREEN'S FUNCTION; LAPLACE TRANSFORMS; PROBABILITY DISTRIBUTIONS; RELIABILITY THEORY; THEOREM PROVING;

BUSY PERIODS; DIFFUSION PROCESS; IDLE PERIODS; PALM PROBABILITY; SPECTRALLY POSITIVE LEVY PROCESSES; STATIONARY PROCESS; STORAGE PROCESS;

QUEUEING THEORY;

EID: 8444219723     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2004.06.005     Document Type: Article

References (15)

1. F. Baccelli, P. Brémaud, Elements of Queueing Theory, 2nd Edition, Springer, Berlin, 2003.
2. B. Bassan, F, Spizzichino, Stochastic comparisons for residual lifetimes and Bayesian notions of multivariate ageing, Adv. Appl. Probab. 31 (1999) 1079-1094.
3. J. Bertoin, Sur la décomposition de la trajectoire d'un processus de Lévy spectralement positif en son minimum, Ann. Inst. H. Poincaré 27 (4) (1991) 537-548.
4. N.H. Bingham, Fluctuation theory in continuous time, Adv, Appl. Probab. 7 (1975) 705-766.
5. A.N. Borodiv, P. Salminen, Handbook of Brownian Motion-Facts and Formulae, 2nd Edition, Birkhäuser, Basel, 2002. ,
6. A. Erdélyi, Tables of Integral Transforms, McGraw-Hill, Now York, 1954.
7. J.M. Harrison, Brownian Motion and Stochastic Flow Systems, Wiley, New York, 1985.
8. K. Itô, H.P. McKean, Diffusion Processes and Their Sample Paths, Springer, Berlin, 1974.
9. P. Mannersalo, I. Norros, P. Salminen, A storage process with local time input, Queueing Systems 46 (2004) 557-577.
10. N.U. Prabhu, Stochastic Storage Processes, 2nd Edition, Springer, New York, 1998.
11. E. Reich, On the integrodifferential equation of Takács I, Ann. Math. Statist. 29 (1958) 563-570.
12. J. Roberts, U. Mocci, J. Virtamo (Eds.), Broadband Network Teletraffic, Lecture Notes in Computer Science, Vol. 1155, Springer, Berlin, 1996.
13. P. Salminen, On the distribution of diffusion local time, Statist. Probab. Lett. 18 (1993) 219-225.
14. P. Salminen, I. Norros, On busy periods of the unbounded Brownian storage, Queueing Systems 39 (2001) 317-333.
15. P. Salminen, P. Vallois, On first range times for linear diffusions, J. Theor. Probab., to appear.