# Anscombe-type theorem and moderate deviations for trajectories of a compound renewal process

## Abstract

An Anscombe-type theorem for the large deviations principle for trajectories of a random process is proved. As a consequence, the moderate deviations principle for the compound renewal processes is obtained.

- Authors:

- Novosibirsk State University of Economy and Management, S. L. Sobolev Institute of Mathematics of the SD of the RAS, Novosibirsk State University, Sibirian State University of Geosystems and Technologies (Russian Federation)
- S. L. Sobolev Institute of Mathematics of the SD of the RAS (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771559

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 229; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; FUNCTIONS; RANDOMNESS; TRAJECTORIES

### Citation Formats

```
Logachov, Artem V., E-mail: omboldovskaya@mail.ru, and Mogulskii, Anatolii A., E-mail: mogul@math.nsc.ru.
```*Anscombe-type theorem and moderate deviations for trajectories of a compound renewal process*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3661-Z.

```
Logachov, Artem V., E-mail: omboldovskaya@mail.ru, & Mogulskii, Anatolii A., E-mail: mogul@math.nsc.ru.
```*Anscombe-type theorem and moderate deviations for trajectories of a compound renewal process*. United States. doi:10.1007/S10958-018-3661-Z.

```
Logachov, Artem V., E-mail: omboldovskaya@mail.ru, and Mogulskii, Anatolii A., E-mail: mogul@math.nsc.ru. Thu .
"Anscombe-type theorem and moderate deviations for trajectories of a compound renewal process". United States. doi:10.1007/S10958-018-3661-Z.
```

```
@article{osti_22771559,
```

title = {Anscombe-type theorem and moderate deviations for trajectories of a compound renewal process},

author = {Logachov, Artem V., E-mail: omboldovskaya@mail.ru and Mogulskii, Anatolii A., E-mail: mogul@math.nsc.ru},

abstractNote = {An Anscombe-type theorem for the large deviations principle for trajectories of a random process is proved. As a consequence, the moderate deviations principle for the compound renewal processes is obtained.},

doi = {10.1007/S10958-018-3661-Z},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 1,

volume = 229,

place = {United States},

year = {2018},

month = {2}

}

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