Exit Times in Non-Markovian Drifting Continuous-Time Random Walk Processes

8 Pages Posted: 3 Feb 2010

See all articles by Miquel Montero

Miquel Montero

University of Barcelona - Departament de Física de la Matèria Condensada

Javier villarroel

affiliation not provided to SSRN

Date Written: February 2, 2010

Abstract

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.

Keywords: continuous-time random walks, non-Markovian processes, exit times

Suggested Citation

Montero, Miquel and villarroel, Javier, Exit Times in Non-Markovian Drifting Continuous-Time Random Walk Processes (February 2, 2010). Available at SSRN: https://ssrn.com/abstract=1546634 or http://dx.doi.org/10.2139/ssrn.1546634

Miquel Montero (Contact Author)

University of Barcelona - Departament de Física de la Matèria Condensada ( email )

Martí i Franquès, 1
Barcelona, Catalonia 08028
Spain
+34 93 403 92 53 (Phone)
+34 93 402 11 55 (Fax)

Javier Villarroel

affiliation not provided to SSRN ( email )

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