Small noise asymptotics for a class of jump-diffusions with heavy tails for large times
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| Format: | Preprint |
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2026
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| _version_ | 1866915849072279552 |
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| author | Anugu, Sumith Reddy Athreya, Siva R. Borkar, Vivek S. |
| author_facet | Anugu, Sumith Reddy Athreya, Siva R. Borkar, Vivek S. |
| contents | In this work, we investigate positive recurrent Lévy diffusions driven by appropriately scaled Brownian motion and $α$-stable process (with $1<α<2$) in the small noise regime. Supposing that in the vanishing noise limit, our Lévy diffusion approaches a deterministic system with a unique asymptotically stable fixed point, we show that the limiting behavior of the one-dimensional marginal distribution at large times is dictated by the optimal value of a deterministic control problem, just as in the classical case of diffusions driven by small variance Brownian motion. In our case, the control is allowed to have two parts: continuous control and impulse control. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_08919 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Small noise asymptotics for a class of jump-diffusions with heavy tails for large times Anugu, Sumith Reddy Athreya, Siva R. Borkar, Vivek S. Probability Optimization and Control Primary: 60F10, Secondary: 60H10, 49N25, 60G52 In this work, we investigate positive recurrent Lévy diffusions driven by appropriately scaled Brownian motion and $α$-stable process (with $1<α<2$) in the small noise regime. Supposing that in the vanishing noise limit, our Lévy diffusion approaches a deterministic system with a unique asymptotically stable fixed point, we show that the limiting behavior of the one-dimensional marginal distribution at large times is dictated by the optimal value of a deterministic control problem, just as in the classical case of diffusions driven by small variance Brownian motion. In our case, the control is allowed to have two parts: continuous control and impulse control. |
| title | Small noise asymptotics for a class of jump-diffusions with heavy tails for large times |
| topic | Probability Optimization and Control Primary: 60F10, Secondary: 60H10, 49N25, 60G52 |
| url | https://arxiv.org/abs/2603.08919 |