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Strong invariance principles for diffusions, Markov chains and their perturbations

  • V. Konakov
  • D. Kucher
  • E. Mammen
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Abstract

In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability of their exact pathwise coincidence on discrete time grids. Moreover, we construct such probability space that the probability of small deviation of the interpolated Markov chain from the continuous diffusion trajectory is small on the entire time interval if the perturbation is small enough.

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Cite

BibTeXRIS
BibTeX
@misc{konakov2026strong,
  title = {{Strong invariance principles for diffusions, Markov chains and their perturbations}},
  author = {V. Konakov and D. Kucher and E. Mammen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.11142},
  eprint = {2606.11142},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.11142},
}
RIS
TY  - UNPB
TI  - Strong invariance principles for diffusions, Markov chains and their perturbations
AU  - V. Konakov
AU  - D. Kucher
AU  - E. Mammen
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2606.11142
UR  - https://arxiv.org/abs/2606.11142
AB  - In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability of their exact pathwise coincidence on discrete time grids. Moreover, we construct such probability space that the probability of small deviation of the interpolated Markov chain from the continuous diffusion trajectory is small on the entire time interval if the perturbation is small enough.
ER  -