2010/02/28 by Miquel Montero, Javier Villarroel
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Computer science #Continuous-time random walk #Erlang (programming language) #Erlang distribution #Exponential distribution #Instant #Jump #Markov process #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Random walk #Renewal theory #Sign (mathematics) #Statistical physics #Statistics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #q-fin.ST
paper · pdf · doi:10.1103/physreve.82.021102
published as Phys. Rev. 82, 021102 (2010) · 9 pages, 3 color plots, two-column revtex 4; new Appendix and references added
arxiv created 2010/06/15 · openalex publication_date 2010/08/04 · arxiv updated 2010/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.