Poisson stability of solutions for stochastic evolution equations driven by fractional Brownian motion
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909355967774720 |
|---|---|
| author | Zhang, Xinze Yong, Li Yang, Xue |
| author_facet | Zhang, Xinze Yong, Li Yang, Xue |
| contents | In this paper, we study the problem of Poisson stability of solutions for stochastic semi-linear evolution equation driven by fractional Brownian motion \mathrm{d} X(t)= \left( AX(t) + f(t, X(t)) \right) \mathrm{d}t + g\left(t, X(t)\right)\mathrm{d}B^H_{Q}(t), where A is an exponentially stable linear operator acting on a separable Hilbert space \mathbb{H}, coefficients f and g are Poisson stable in time, and B^H_Q (t) is a Q-cylindrical fBm with Hurst index H. First, we establish the existence and uniqueness of the solution for this equation. Then, we prove that under the condition where the functions f and g are sufficiently "small", the equation admits a solution that exhibits the same character of recurrence as f and g. The discussion is further extended to the asymptotic stability of these Poisson stable solutions. Finally, we include an example to validate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poisson stability of solutions for stochastic evolution equations driven by fractional Brownian motion Zhang, Xinze Yong, Li Yang, Xue Dynamical Systems Analysis of PDEs Probability 60G22, 34C25, 34C27, 37B20, 60H10, 34D20 In this paper, we study the problem of Poisson stability of solutions for stochastic semi-linear evolution equation driven by fractional Brownian motion \mathrm{d} X(t)= \left( AX(t) + f(t, X(t)) \right) \mathrm{d}t + g\left(t, X(t)\right)\mathrm{d}B^H_{Q}(t), where A is an exponentially stable linear operator acting on a separable Hilbert space \mathbb{H}, coefficients f and g are Poisson stable in time, and B^H_Q (t) is a Q-cylindrical fBm with Hurst index H. First, we establish the existence and uniqueness of the solution for this equation. Then, we prove that under the condition where the functions f and g are sufficiently "small", the equation admits a solution that exhibits the same character of recurrence as f and g. The discussion is further extended to the asymptotic stability of these Poisson stable solutions. Finally, we include an example to validate our results. |
| title | Poisson stability of solutions for stochastic evolution equations driven by fractional Brownian motion |
| topic | Dynamical Systems Analysis of PDEs Probability 60G22, 34C25, 34C27, 37B20, 60H10, 34D20 |
| url | https://arxiv.org/abs/2407.04313 |