Opuscula Math. 30, no. 3 (2010), 255-270

Opuscula Mathematica

On the approximation theorem of Wong-Zakai type for the Lasota operator

Antoni Leon Dawidowicz
Krystyna Twardowska

Abstract. We consider in this paper a stochastic evolution equation with Professor A. Lasota's operator as the infinitesimal generator of a strongly continuous semigroup of transformations and with Hammerstein operator connected with a noise being the Wiener process. We show that such evolution equation satisfies the Wong-Zakai type approximation theorem. The idea of the definition of the Lasota operator has the origin in the mathematical model of the creation and differentiation of cells in biology and medicine.

Keywords: stochastic evolution equations, Wong-Zakai approximations, Lasota operator.

Mathematics Subject Classification: 60H20, 37A10, 60H10, 60H25, 35A08.

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  • Antoni Leon Dawidowicz
  • Jagellonian University, Institute of Mathematics, ul. Łojasiewicza 6, 30-348 Cracow, Poland
  • Krystyna Twardowska
  • Warsaw University of Life Sciences – SGGW, Faculty of Applied Informatics and Mathematics, ul. Nowoursynowska 159, 02-776 Warsaw, Poland
  • Received: 2010-01-08.
  • Accepted: 2010-03-16.
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Cite this article as:
Antoni Leon Dawidowicz, Krystyna Twardowska, On the approximation theorem of Wong-Zakai type for the Lasota operator, Opuscula Math. 30, no. 3 (2010), 255-270, http://dx.doi.org/10.7494/OpMath.2010.30.3.255

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