Stochastic Bernoulli equation on the algebra of generalized functions
UDC 519.21 Based on the topological dual space $\mathcal{F}_\theta^*(\mathcal{S'}_{\mathbb{C}})$ of the space of entire functions  with $\theta$-exponential growth of finite type, we introduce the generalized stochastic Bernoulli–Wick differential equation (or the stochastic Be...
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| Datum: | 2023 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7223 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 519.21
Based on the topological dual space $\mathcal{F}_\theta^*(\mathcal{S'}_{\mathbb{C}})$ of the space of entire functions  with $\theta$-exponential growth of finite type, we introduce the generalized stochastic Bernoulli–Wick differential equation (or the stochastic Bernoulli equation on the algebra of generalized functions) by using the Wick product of elements in $\mathcal{F}_\theta^*(\mathcal{S'}_{\mathbb{C}})$. This equation is an infinite-dimensional stochastic distributions analog of  the classical  Bernoulli differential equation. This stochastic differential equation is solved  and exemplified by several examples. |
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| DOI: | 10.3842/umzh.v75i8.7223 |