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Stochastic Clairaut Equation on Algebra of Generalized Functions

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Abstract

Based on an infinite dimensional distributions space, we study the solution of the generalized stochastic Clairaut equation using a suitable convolution calculus. The solution of such equation is shown to be positive and its integral representation with respect to the Radon measure is given. Moreover, the contractivity property is studied. Finally, the system is shown to be finite-time stochastically stable.

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Authors and Affiliations

  1. Department of Mathematics, Al-Qunfudhah University College, Umm Al-Qura University, Mecca, Kingdom of Saudi Arabia

    Hafedh Rguigui

  2. High School of Sciences and Technology of Hammam Sousse, University of Sousse, Rue Lamine Abassi, 4011, Hammam Sousse, Tunisia

    Hafedh Rguigui

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  1. Hafedh Rguigui
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HR did this work.

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Correspondence to Hafedh Rguigui.

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Communicated by Palle Jorgensen.

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This article is part of the topical collection “Infinite-dimensional Analysis and Non-commutative Theory” edited by Marek Bozejko, Palle Jorgensen and Yuri Kondratiev.

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Rguigui, H. Stochastic Clairaut Equation on Algebra of Generalized Functions. Complex Anal. Oper. Theory 18, 19 (2024). https://doi.org/10.1007/s11785-023-01466-1

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