Young differential equations driven by Besov–Orlicz paths

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F25%3A00638624" target="_blank" >RIV/67985556:_____/25:00638624 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/25:10501389
Result on the web
<a href="https://www.aimsciences.org//article/doi/10.3934/dcdsb.2025044" target="_blank" >https://www.aimsciences.org//article/doi/10.3934/dcdsb.2025044</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcdsb.2025044" target="_blank" >10.3934/dcdsb.2025044</a>

Result language
angličtina
Original language name
Young differential equations driven by Besov–Orlicz paths
Original language description
In the article, we consider nonlinear differential equations driven by paths from the exponential Besov–Orlicz space $B^alpha_{Phi_beta,q}$ for $alpha in (1/2, 1)$, $Phi_beta(x) sim e^{x^beta} - 1$ with $beta in (0, infty)$, and $q in (0, infty]$. By appealing to the recently obtained sewing lemma for such paths, we construct a Young-type integral and show that such equations admit a unique solution that is again of exponential Besov–Orlicz regularity. The results cover equations driven by paths of a large number of stochastic processes that exhibit long-range dependence, e.g. fractional Brownian motion with Hurst parameter $H in (1/2, 1)$ or, more generally, any Hermite process.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA22-12790S" target="_blank" >GA22-12790S: Stochastic systems in infinite dimensions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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