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- W2286076895 abstract "In this note we consider SDEs of the type $mathrm{d} X_t=[F (X_t) -A X_t] mathrm{d} t +D mathrm{d} W_t$ under the assumptions that $A$'s eigenvalues are all of positive real parts and $F (cdot)$ has slower-than-linear growth rate. It is proved that $displaystyle varlimsup_{t to infty} frac{|X_t|}{sqrt{log t}} =sqrt{2 lambda_1}$ almost surely with $lambda_1$ being the largest eigenvalue of the matrix $displaystyle Sigma :=int_0^infty e^{-s A} cdot (D cdot D^T) cdot e^{-s A^T} mathrm{d} s$; the discarded measure-zero set can be chosen independent of the initial values $X_0=x$." @default.
- W2286076895 created "2016-06-24" @default.
- W2286076895 creator A5010663997 @default.
- W2286076895 date "2014-07-10" @default.
- W2286076895 modified "2023-10-14" @default.
- W2286076895 title "Bounding Ornstein-Uhlenbeck Processes and Alikes" @default.
- W2286076895 cites W1525362755 @default.
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- W2286076895 doi "https://doi.org/10.48550/arxiv.1407.2725" @default.
- W2286076895 hasPublicationYear "2014" @default.
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