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We give an asymptotic expression for the tail of the maximum of Brownian motion minus a parabola. This confirms a conjecture about the exponential term in the tail behavior, due to Svante Janson.
We derive a simple integral representation for the distribution of the maximum of Brownian motion minus a parabola, which can be used for computing the density and moments of the distribution, both fo...
The Nyström method for functional quantization with an application to the fractional Brownian motion
integral equation Nyströ m method Gaussian semi-martingale functional quantization
2010/12/1
In this article, the so-called "Nyström method" is tested to compute optimal quantizers of Gaussian processes. In particular, we derive the optimal quantization of the fractional Brownian motion ...
Isolated zeros for Brownian motion with variable drift
Brownian motion H¨older continuity Cantor function
2010/12/8
It is well known that standard one-dimensional Brownian motion B(t) has no isolated zeros almost surely. We show that for any < 1/2 there are -H¨older continuous functions f(t) for which the proces...
Dimensional Properties of Fractional Brownian Motion
fractional Brownian motion Hausdorff dimension uniform dimension results strong local nondeterminism
2007/12/11
Let $B^\a = \{B^{\alpha}(t), t \in {\mathbb R}^N\}$ be an $(N,d)$-fractional Brownian motion with Hurst index ${\alpha} \in (0,1)$. By applying the strong local nondeterminism of $B^{\alpha}$, we prov...