The weak convergence of regenerative processes using some excursion path decompositions

A. Lambert, F. Simatos

Research output: Book/ReportReportAcademic

Abstract

We consider regenerative processes with values in some Polish space. We define their \epsilon-big excursions as excursions e such that f(e)>\epsilon, where f is some given functional on the space of excursions which can be thought of as, e.g., the length or the height of e. We establish a general condition that guarantees the convergence of a sequence of regenerative processes involving the convergence of \epsilon-big excursions and of their endpoints, for all \epsilon in a countable set whose closure contains 0. Finally, we provide various sufficient conditions on the excursion measures of this sequence for this general condition to hold and discuss possible generalizations of our approach to processes that can be written as the concatenation of i.i.d. paths.
Original languageEnglish
Publishers.n.
Number of pages21
Publication statusPublished - 2012

Publication series

NamearXiv
Volume1202.2878 [math.PR]

Fingerprint

Path Decomposition
Regenerative Process
Excursion
Weak Convergence
Polish Space
Concatenation
Countable
Closure
Path
Sufficient Conditions

Cite this

Lambert, A., & Simatos, F. (2012). The weak convergence of regenerative processes using some excursion path decompositions. (arXiv; Vol. 1202.2878 [math.PR]). s.n.
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Lambert, A & Simatos, F 2012, The weak convergence of regenerative processes using some excursion path decompositions. arXiv, vol. 1202.2878 [math.PR], s.n.

The weak convergence of regenerative processes using some excursion path decompositions. / Lambert, A.; Simatos, F.

s.n., 2012. 21 p. (arXiv; Vol. 1202.2878 [math.PR]).

Research output: Book/ReportReportAcademic

TY - BOOK

T1 - The weak convergence of regenerative processes using some excursion path decompositions

AU - Lambert, A.

AU - Simatos, F.

PY - 2012

Y1 - 2012

N2 - We consider regenerative processes with values in some Polish space. We define their \epsilon-big excursions as excursions e such that f(e)>\epsilon, where f is some given functional on the space of excursions which can be thought of as, e.g., the length or the height of e. We establish a general condition that guarantees the convergence of a sequence of regenerative processes involving the convergence of \epsilon-big excursions and of their endpoints, for all \epsilon in a countable set whose closure contains 0. Finally, we provide various sufficient conditions on the excursion measures of this sequence for this general condition to hold and discuss possible generalizations of our approach to processes that can be written as the concatenation of i.i.d. paths.

AB - We consider regenerative processes with values in some Polish space. We define their \epsilon-big excursions as excursions e such that f(e)>\epsilon, where f is some given functional on the space of excursions which can be thought of as, e.g., the length or the height of e. We establish a general condition that guarantees the convergence of a sequence of regenerative processes involving the convergence of \epsilon-big excursions and of their endpoints, for all \epsilon in a countable set whose closure contains 0. Finally, we provide various sufficient conditions on the excursion measures of this sequence for this general condition to hold and discuss possible generalizations of our approach to processes that can be written as the concatenation of i.i.d. paths.

M3 - Report

T3 - arXiv

BT - The weak convergence of regenerative processes using some excursion path decompositions

PB - s.n.

ER -