Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.04865 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912868061937664 |
|---|---|
| author | Rybakov, Konstantin A. |
| author_facet | Rybakov, Konstantin A. |
| contents | This article proposes a method for forming invariant stochastic differential systems, namely dynamic systems with trajectories belonging to a given smooth manifold. The Itô or Stratonovich stochastic differential equations with the Wiener component describe dynamic systems, and the manifold is implicitly defined by a differentiable function. A convenient implementation of the algorithm for forming invariant stochastic differential systems within symbolic computation environments characterizes the proposed method. It is based on determining a basis associated with a tangent hyperplane to the manifold. The article discusses the problem of basis degeneration and examines variants that allow for the simple construction of a basis that does not degenerate. Examples of invariant stochastic differential systems are given, and numerical simulations are performed for them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04865 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Forming invariant stochastic differential systems with a given first integral Rybakov, Konstantin A. Probability 58J65, 60H10 G.3 This article proposes a method for forming invariant stochastic differential systems, namely dynamic systems with trajectories belonging to a given smooth manifold. The Itô or Stratonovich stochastic differential equations with the Wiener component describe dynamic systems, and the manifold is implicitly defined by a differentiable function. A convenient implementation of the algorithm for forming invariant stochastic differential systems within symbolic computation environments characterizes the proposed method. It is based on determining a basis associated with a tangent hyperplane to the manifold. The article discusses the problem of basis degeneration and examines variants that allow for the simple construction of a basis that does not degenerate. Examples of invariant stochastic differential systems are given, and numerical simulations are performed for them. |
| title | Forming invariant stochastic differential systems with a given first integral |
| topic | Probability 58J65, 60H10 G.3 |
| url | https://arxiv.org/abs/2601.04865 |