MA(1) processes with Laplace innovations conditioned to stay positive
Abstract
We study a moving-average process with (not necessarily symmetric) Laplace innovations under the constraint of positivity. In the three nondegenerate parameter regimes 0<θ<1, θ>1, and θ<0, we prove convergence of the conditioned finite-dimensional distributions and identify the limit as a Doob h-transform. The regimes lead to qualitatively different limiting dynamics: the invariant law is supported on the positive half-line for 0<θ<1, the conditioned chain is confined to the negative half-line for θ>1, and the dynamics are genuinely two-sided and governed by q-trigonometric functions for θ<0. In each case, the persistence exponent, sharp persistence asymptotics, the defining eigenfunction, and the unique invariant distribution are obtained explicitly.
Related
- Asymptotic expansions for random walks conditioned to stay positive with arbitrary endpoints
- Persistence probabilities of MA(1) sequences with Laplace innovations and q-deformed zigzag numbers
- Continuous-state branching processes with Lévy-Khintchine drift-interaction: Laplace duality and Fellerian extensions
- Limit theory for a class of non-stationary linear processes with weakly dependent heavy-tailed innovations
- The Askey-Wilson Function is the Laplace Transform of a Positive Measure
BibTeX
@misc{aurzada2026processes,
title = {{MA(1) processes with Laplace innovations conditioned to stay positive}},
author = {Frank Aurzada and Virginia Worf},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08794},
eprint = {2609.08794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08794},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - MA(1) processes with Laplace innovations conditioned to stay positive
AU - Frank Aurzada
AU - Virginia Worf
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08794
UR - https://arxiv.org/abs/2609.08794
AB - We study a moving-average process with (not necessarily symmetric) Laplace innovations under the constraint of positivity. In the three nondegenerate parameter regimes 0<θ<1, θ>1, and θ<0, we prove convergence of the conditioned finite-dimensional distributions and identify the limit as a Doob h-transform. The regimes lead to qualitatively different limiting dynamics: the invariant law is supported on the positive half-line for 0<θ<1, the conditioned chain is confined to the negative half-line for θ>1, and the dynamics are genuinely two-sided and governed by q-trigonometric functions for θ<0. In each case, the persistence exponent, sharp persistence asymptotics, the defining eigenfunction, and the unique invariant distribution are obtained explicitly.
ER -