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Sticky Brownian Motion with a Locally Finite Atomic Sticky Measure
Abstract
We study sticky Brownian motion on ℝ with a set of sticky points A. In contrast to the classical case of a single sticky point, the set A may have a more complicated structure and, in particular, may have accumulation points. The stickiness at the points of A is described by a locally finite purely atomic measure ν. We extend the classical time-change approach for sticky Brownian motion to this setting and use it to construct a weak solution of the corresponding stochastic differential equation with a local-time condition. We then prove uniqueness in law of the solution.
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BibTeX
@misc{jafarova2026sticky,
title = {{Sticky Brownian Motion with a Locally Finite Atomic Sticky Measure}},
author = {L. A. Jafarova},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24740},
eprint = {2609.24740},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24740},
}
RIS
TY - UNPB
TI - Sticky Brownian Motion with a Locally Finite Atomic Sticky Measure
AU - L. A. Jafarova
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24740
UR - https://arxiv.org/abs/2609.24740
AB - We study sticky Brownian motion on ℝ with a set of sticky points A. In contrast to the classical case of a single sticky point, the set A may have a more complicated structure and, in particular, may have accumulation points. The stickiness at the points of A is described by a locally finite purely atomic measure ν. We extend the classical time-change approach for sticky Brownian motion to this setting and use it to construct a weak solution of the corresponding stochastic differential equation with a local-time condition. We then prove uniqueness in law of the solution.
ER -