REFERENCES

[1] Agarwal, R.P., Dshalalow, J.H., and O’Regan, D., Time sensitive functionals of

marked Cox processes, Journ. of Math. Analysis and Appl., 293 (2004), 14-27.

[2] Al-Matar, N. and Dshalalow, J.H., A game-theoretic approach in single-server

queues with maintenance. Time sensitive analysis, Commun. in Appl. Nonlin. Analysis, 17, No. 1 (2010), 65-92.

[3] Al-Matar, N. and Dshalalow, J.H., Time sensitive functionals in classes of queues

with sequential maintenance, Stochastic Models, 27 (2011), 687–704.

[4] Atiya, A.F. and Metwally, S.A., Efficient estimation of first passage time density

function for jump-diffusion processes, SIAM J. Sci. Comput., 26(5), 1760–1775.

[5] Aurzada, F., Iksanov, A., and Meiners, M., Exponential moments of first passage

times and related quantities for L´evy processes, Mathematische Nachrichten

(2015), (DOI: 10.1002/mana.201400289).

[6] Bingham, N.H., Random walk and fluctuation theory, in Handbook of Statistics

(Eds. D.N. Shanbhag and C.R. Rao), Volume 19, 2001, Elsevier Science, 171-213.

[7] Borokov, A.A., On the first passage time for one class of processes with independent

increments. Theor. Probab. Appl., 10 (1964), 331–334.

[8] Coutin, L. and Dorobantu, D., First passage time law for some Levy processes

with compound Poisson: Existence of a density, Bernoulli, 17:4 (2011), 1127- 1135.

[9] Crescenzo, A.D. and Martinucci, B., On a first passage-time problem for the

compound power-law process, Stochastic Models, 25 (2009), 420-435.

[10] Dshalalow, J.H., First excess level of v

[19] Dshalalow, J.H., Iwezulu, K., and White, R.T., Discrete operational calculus

in delayed stochastic games, Neural, Parallel, and Scientific Computations, 24 (2016), 55-64.

[20] Dshalalow, J.H. and Ke, H.-J., Multilayers in a modulated stochastic game,

Journ. of Math. Analysis and Applications, 353 (2009), 553-565.

[21] Dshalalow, J.H. and Liew, A., On exit time of a multivariate random walk and

its embedding in a quasi-Poisson process, Stochastic Analysis and Applications,

24 (2006), 451-474.

[22] Dshalalow, J.H. and White, R.T., On reliability of stochastic networks, Neural,

Parallel, and Scientific Computations, 21 (2013) 141-160.

[23] Dshalalow, J.H. and White, R.T., On strategic defense in stochastic networks,

Stochastic Analysis and Applications, 32 (2014), 365–396.

[24] Dshalalow, J.H. and White, R.T., Time sensitive analysis of independent and stationary

increment processes, Journal of Mathematical Analysis and Applications

443 (2016), 817-833.

[25] Hida, T. (Editor), Mathematical Approach to Fluctuations: Astronomy, Biology

and Quantum Dynamics: Proceedings of the Iias Workshop: Kyoto, Japan, May

18-21, 1992, World Scientific Publishers, 1995).

[26] Fishburn, P.C., Non-cooperative stochastic dominance games, International Journal

of Game Theory, 7:1 (1978), 51-61.

[27] Kadankova, T.V., Exit, passage, and crossing times and overshoots for a Poisson

compound process with an exponential component, Theor. Probability and

Math. Statist., 75 (2007), 23-29.

[28] Kyprianou, A.E. and Pistorius, M.R., Perpetual options and Canadization through

fluctuation theory, Ann. Appl. Prob., 13:3 (2003), 1077-1098.

[29] Mellander, E., Vredin, A, and Warne, A., Stochastic trends and economic fluctuations

in a small open economy, J. Applied Econom., 7:4 (1992), 369-94.

[30] Muzy, J., Delour1, J., and Bacry, E., Modelling fluctuations of financial time

series: from cascade process to stochastic volatility model, Eur. Phys. J. B 17 (2000), 537-548.

[31] Novikov, A, Melchers, R.E., Shinjikashvili, E., and Kordzakhia, N., First passage

time of filtered Poisson process with exponential shape function, Probabilistic

Engineering Mechanics, 20:1 (2005), 57-65

[32] Redner, S., A Guide to First-Passage Processes, Cambridge University Press,

Cambridge, 2001.

[33] Shinozuka, M. and Wu, W-F., On the first passage problem and its application to

earthquake engineering, Proceedings of Ninth World Conference on Earthquake

Engineering, August 2-9, (VIII) 1988, Tokyo-Kyoto, Japan.

[34] Tak´acs, L., On fluctuations of sums of random variables, in Studies in Probability

and Ergodic Theory. Advances in Mathematics; Supplementary Studies, Volume

2, ed. by G.-C. Rota, (1978), 45-93.

[35] Yin, C., Wen, Y., Zong, Z., and Shen, Y., The first passage time problem for

mixed-exponential jump processes with applications in insurance and finance,

Abstract and Applied Analysis (2014), 9 pages.

[36] Zolotarev, V.M. The first passage time of a level and the behavior at infnity for a

class of processes with independent increments, Theor. Probab. Appl, 9 (1964)

653–664.