dorsal/arxiv
View SchemaMemory functions and Correlations in Additive Binary Markov Chains
| Authors | S. S. Melnyk, O. V. Usatenko, V. A. Yampol'skii, S. S. Apostolov, Z. A. Mayzelis |
|---|---|
| Categories | |
| ArXiv ID | physics/0603171 |
| URL | https://arxiv.org/abs/physics/0603171 |
| DOI | 10.1088/0305-4470/39/46/004 |
Abstract
A theory of additive Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such systems, a memory function, and its relation to the correlation properties of the systems are examined. Various methods for finding the memory function via the correlation function are proposed. The inverse problem (calculation of the correlation function by means of the prescribed memory function) is also solved. This is demonstrated for the analytically solvable model of the system with a step-wise memory function.
{
"annotation_id": "09caf66c-3ba4-4b60-b162-3cc2079bd8ab",
"date_created": "2026-03-02T18:01:07.846000Z",
"date_modified": "2026-03-02T18:01:07.846000Z",
"file_hash": "e1e603fb2e8eaffcf8f1cdaa2b1944db5466e4e58c0c41f7337c1817a03f0cbb",
"private": false,
"record": {
"abstract": "A theory of additive Markov chains with long-range memory, proposed earlier\nin Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical\nproperties of long-range correlated systems. The convenient characteristics of\nsuch systems, a memory function, and its relation to the correlation properties\nof the systems are examined. Various methods for finding the memory function\nvia the correlation function are proposed. The inverse problem (calculation of\nthe correlation function by means of the prescribed memory function) is also\nsolved. This is demonstrated for the analytically solvable model of the system\nwith a step-wise memory function.",
"arxiv_id": "physics/0603171",
"authors": [
"S. S. Melnyk",
"O. V. Usatenko",
"V. A. Yampol\u0027skii",
"S. S. Apostolov",
"Z. A. Mayzelis"
],
"categories": [
"physics.data-an",
"physics.gen-ph"
],
"doi": "10.1088/0305-4470/39/46/004",
"title": "Memory functions and Correlations in Additive Binary Markov Chains",
"url": "https://arxiv.org/abs/physics/0603171"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "91e682e2-9b43-41a5-916a-753730325699",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}