Ladder height process

In probability theory, the ladder height process is a record of the largest or smallest value a given stochastic process has achieved up to the specified point in time.^[1]

The Wiener-Hopf factorization gives the transition probability kernel in the discrete time case.^[2]

References

^ Asmussen, S. R. (2003). "Random Walks". Applied Probability and Queues. Stochastic Modelling and Applied Probability. Vol. 51. pp. 220–243. doi:10.1007/0-387-21525-5_8. ISBN 978-0-387-00211-8.
^ Miyazawa, M. (2002). "A paradigm of Markov additive processes for queues and their networks". Matrix-Analytic Methods - Theory and Applications - Proceedings of the Fourth International Conference. pp. 265–289. doi:10.1142/9789812777164_0015. ISBN 9789812380517.

[1] Asmussen, S. R. (2003). "Random Walks". Applied Probability and Queues. Stochastic Modelling and Applied Probability. Vol. 51. pp. 220–243. doi:10.1007/0-387-21525-5_8. ISBN 978-0-387-00211-8.

[2] Miyazawa, M. (2002). "A paradigm of Markov additive processes for queues and their networks". Matrix-Analytic Methods - Theory and Applications - Proceedings of the Fourth International Conference. pp. 265–289. doi:10.1142/9789812777164_0015. ISBN 9789812380517.

[1]

[2]

See also

References