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Mild Solution of Semilinear SPDEs with Young Drifts
- Publication Year :
- 2023
-
Abstract
- In this paper, we study a semilinear SPDE with a linear Young drift $du_{t}=Lu_{t}dt+f\left(t, u_{t}\right)dt+\left(G_{t}u_{t}+g_{t}\right)d\eta_{t}+h\left(t, u_{t}\right)dW_{t}$, where $L$ is the generator of an analytical semigroup, $\eta$ is an $\alpha$-H\"older continuous path with $\alpha \in \left(1/2, 1\right)$ and $W$ is a Brownian motion. After establishing through two different approaches the Young convolution integrals for stochastic integrands, we introduce the corresponding definition of mild solutions and continuous mild solutions, and give via a fixed-point argument the existence and uniqueness of the (continuous) mild solution under suitable conditions.<br />Comment: 17 pages
- Subjects :
- Mathematics - Probability
60H15, 60L50
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2309.06791
- Document Type :
- Working Paper