Stochastic Bernoulli equation on the algebra of generalized functions

  • Hafedh Rguigui Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, KSA, High School of Sciences and Technology of Hammam Sousse, University of Sousse, Hammam Sousse, Tunisia
Keywords: Wick product; Generalized stochastic Bernoulli Wick differential equation; Space of entire functions with $\theta$-exponential growth condition of minimal type.


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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How to Cite
Rguigui, H. “Stochastic Bernoulli Equation on the Algebra of Generalized Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 8, Aug. 2023, pp. 1085 -95, doi:10.3842/umzh.v75i8.7223.
Research articles