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![Figure 5: Interbeat intervals from a diseased heart (up) and from a healthy heart (down) from[Buc98].](https://thumb-ap.123doks.com/thumbv2/123dok/983038.916544/24.612.177.417.92.329/figure-interbeat-intervals-diseased-heart-healthy-heart-buc.webp)
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Path transformations have proved useful in the study of Brownian motion and related pro- cesses, by providing simple constructions of various conditioned processes such as
Key words: stochastic differential equations, Brownian motion, Law of the Iterated Logarithm, Motoo’s theorem, stochastic comparison principle, stationary processes,
Keywords: Gaussian random walk; maximum; Riemann zeta function; Euler-Maclaurin summa- tion; equidistant sampling of Brownian motion; finite
In order to identify the limit, we shall characterize the limit as the unique solution of the aforementioned SDE-like equation (cf. the initial position of a reflected Brownian
Lawler (1990): Non-intersection exponents for random walk and Brownian motion. Part II: Estimates and applications to a random
This result has consequences for the Hausdorff dimension of the frontier of planar Brownian motion, and also for the Hausdorff dimension of the set of cut-points of planar
Our proof follows recent work by Denisov and Wachtel who used mar- tingale properties and a strong approximation of random walks by Brownian motion.. Therefore, we are able to
We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to
