Sticky-Reflected Stochastic Heat Equation Driven by Colored Noise

Konarovskyi V (2021)
Ukrainian Mathematical Journal 72(9): 1377-1419.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Einrichtung
Abstract / Bemerkung
We prove the existence of a sticky-reflected solution to the heat equation on the space interval [0, 1] driven by colored noise. The process can be interpreted as an infinite-dimensional analog of the sticky-reflected Brownian motion on the real line but, in this case, the solution obeys the ordinary stochastic heat equation, except the points where it reaches zero. The solution has no noise at zero and a drift pushes it to stay positive. The proof is based on a new approach that can also be applied to some other types of SPDEs with discontinuous coefficients.
Erscheinungsjahr
2021
Zeitschriftentitel
Ukrainian Mathematical Journal
Band
72
Ausgabe
9
Seite(n)
1377-1419
ISSN
0041-5995
eISSN
1573-9376
Page URI
https://pub.uni-bielefeld.de/record/2957870

Zitieren

Konarovskyi V. Sticky-Reflected Stochastic Heat Equation Driven by Colored Noise. Ukrainian Mathematical Journal. 2021;72(9):1377-1419.
Konarovskyi, V. (2021). Sticky-Reflected Stochastic Heat Equation Driven by Colored Noise. Ukrainian Mathematical Journal, 72(9), 1377-1419. https://doi.org/10.1007/s11253-021-01863-9
Konarovskyi, V. (2021). Sticky-Reflected Stochastic Heat Equation Driven by Colored Noise. Ukrainian Mathematical Journal 72, 1377-1419.
Konarovskyi, V., 2021. Sticky-Reflected Stochastic Heat Equation Driven by Colored Noise. Ukrainian Mathematical Journal, 72(9), p 1377-1419.
V. Konarovskyi, “Sticky-Reflected Stochastic Heat Equation Driven by Colored Noise”, Ukrainian Mathematical Journal, vol. 72, 2021, pp. 1377-1419.
Konarovskyi, V.: Sticky-Reflected Stochastic Heat Equation Driven by Colored Noise. Ukrainian Mathematical Journal. 72, 1377-1419 (2021).
Konarovskyi, Vitalii. “Sticky-Reflected Stochastic Heat Equation Driven by Colored Noise”. Ukrainian Mathematical Journal 72.9 (2021): 1377-1419.

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