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The tail of the maximum of Brownian motion minus a parabola     Brownian motion  parabola       font style='font-size:12px;'> 2010/11/23
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.
Is Brownian motion necessary to model high-frequency data?     Brownian motion  high-frequency data       font style='font-size:12px;'> 2010/11/18
This paper considers the problem of testing for the presence of a continuous part in a semimartingale sampled at high frequency. We provide two tests, one where the null hypothesis is that a continuou...
The maximum of Brownian motion minus a parabola     Brownian motion   parabola       font style='font-size:12px;'> 2010/11/8
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 greatest convex minorant of Brownian motion, meander, and bridge     convex minorant  Brownian motion       font style='font-size:12px;'> 2010/11/19
This article contains both a point process and a sequential description of the greatest convex minorant of Brownian motion on a finite interval. We use these descriptions to provide new analysis of v...
Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations hx(t1)x(t2)i = Dt2H 1 + t2H 2 􀀀 jt1 􀀀 t2j2H, where H, with 0 < H < 1 is called the Hu...
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 ...
Survival of near-critical branching Brownian motion      ival  near-critical branching Brownian motion        font style='font-size:12px;'> 2010/11/29
Consider a system of particles performing branching Brownian motion with negative drift μ = √2 − " and killed upon hitting zero. Initially there is one particle at x > 0. Kesten [12] showed th...
Isolated zeros for Brownian motion with variable drift      Brownian motion  H¨older continuity  Cantor function       font style='font-size:12px;'> 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...
Consider a semimartingale reflecting Brownian motion (SRBM)Z whose state space is the d-dimensional nonnegative orthant. The data for such a process are a drift vector , a nonsingular d×d covariance ...
We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of L&acut...
Advective skew dispersion is a natural Markov process defined by a diffusion with drift across an interface of jump discontinuity in a piecewise constant diffusion coefficient.
Considering quantum random walks, we construct discrete-time approximations of the eigenvalues processes of minors of Hermitian Brownian motion.
Further remarks on mixed fractional Brownian motion     Fractional Brownian Motion  Fractional Calculus       font style='font-size:12px;'> 2010/9/15
We study linear combinations of independent fractional Brownian motions and generalize several recent results from [10] and [17]. As a first new result we calculate explicitly the Hausdorff dimension ...
In this paper, we present some stochastic properties and characteristics of the fractional mixed fractional Brownian motion, and we study the α-differentiability of its sample paths.
The dimensions of the level sets of the generalized iterated Brownian motion.

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