On the Generalized Telegraph Process with Deterministic Jumps

Abramowitz M, Stegun IA (1992) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover, New York

Beghin L, Nieddu L, Orsingher E (2001) Probabilistic analysis of the telegrapher’s process with drift by means of relativistic transformations. J Appl Math Stoch Anal 14:11–25

Boxma O, Perry D, Stadje W, Zacks S (2006) A Markovian growth-collapse model. Adv Appl Probab 38:221–243

Di Crescenzo A (2001) On random motions with velocities alternating at Erlang-distributed random times. Adv Appl Probab 33:690–701

Di Crescenzo A, Martinucci B (2010) A damped telegraph random process with logistic stationary distribution. J Appl Probab 47:84–96

Di Crescenzo A, Pellerey F (2002) On prices’ evolutions based on geometric telegrapher’s process. Appl Stoch Models Bus Ind 18:171–184

Goldstein S (1951) On diffusion by discontinuous movements and the telegraph equation. Q J Mech Appl Math 4:129–156

Kac M (1974) A stochastic model related to the telegrapher’s equation. Rochy Mountain J Math 4:497–509

Lachal A (2006) Cyclic random motions in ℝ d -space with n directions. ESAIM Probab Stat 10:277–316

Mazza C, Rullière D (2004) A link between wave governed random motions and ruin processes. Insur, Math Econ 35:205–222

Orsingher E (1990a) Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchoff’s laws. Stoch Process Their Appl 34:49–66

Orsingher E (1990b) Random motions governed by third-order equations. Adv Appl Probab 22:915–928

Pellerey F, Shaked M (1993) Stochastic comparison of some wear processes. Probab Eng Inf Sci 7:421–435

Pellerey F, Shaked M (1996) Stochastic comparison of processes generated by random interruptions of monotone functions and related results. Lifetime Data Anal 2:91–112

Perry D, Stadje W, Zacks S (2002) First-exit times for compound Poisson processes for some types of positive and negative jumps. Stoch Models 18:139–157

Perry D, Stadje W, Zacks S (2005) A two-sided first-exit problem for a compound Poisson process with a random upper boundary. Methodol Comput Appl Probab 7:51–62

Ratanov N (2007a) A jump telegraph model for option pricing. Quantitative Finance 7:575–583

Ratanov N (2007b) Jump telegraph processes and financial markets with memory. J Appl Math Stoch Anal. doi: 10.1155/2007/72326

Ratanov N, Melnikov A (2008) On financial markets based on telegraph processes. Stochastics 80:247–268

Stadje W, Zacks S (2004) Telegraph processes with random velocities. J Appl Probab 41:665–678

Zacks S (2004) Generalized integrated telegrapher process and the distribution of related stopping times. J Appl Probab 41:497–507