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Let $B(t)$ be a Brownian motion in $R^3$. A {it subpath} of the Brownian path $B[0,1]$ is a continuous curve $gamma(t)$, where $gamma[0,1] subseteq B[0,1]$ , $gamma(0) = B(0)$, and $gamma(1) = B(1)$. ...
Given a standard Brownian motion $B$, we show that the equation X_t = x_0 + B_t + beta(L_t^X), t geq 0, has a unique strong solution $X$. Here $L^X$ is the symmetric local time of $X$ at $0$, and ...
A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian mo- tion and its s...
We give a new representation of fractional Brownian motion with Hurst parameter $Hleqfrac{1}{2}$ using stochastic partial differential equations. This representation allows us to use the Markov proper...
We define a Fractional Brownian Motion indexed by a sphere, or more generally by a compact rank one symmetric space, and prove that it exists if, and only if, 0< H leq 1/2. We then prove that Fraction...
Let B be a standard Brownian motion and let b_gamma be a piecewise linear continuous boundary function. In this paper we obtain an exact asymptotic expansion of P{ B(t)< b_gamma(t), forall tin [0,1]} ...
We use excursion theory and the ergodic theorem to present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. A simplified version of our method also p...
The purpose of this work is to study some possible application of FKG inequality to the Brownian motion and to Stochastic Differential Equations. We introduce a special ordering on the Wiener space an...
We derive the asymptotic behavior of the total occupation measure of the unit ball for super-Brownian motion started from the Dirac measure at a distant point and conditioned to hit the unit ball. In ...
We give a simple proof that in a Lipschitz domain in two dimensions with Lipschitz constant one, there is pathwise uniqueness for the Skorokhod equation governing reflecting Brownian motion.
A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian mo- tion and its s...
We give a new representation of fractional Brownian motion with Hurst parameter $Hleqfrac{1}{2}$ using stochastic partial differential equations. This representation allows us to use the Markov proper...
We give necessary and sufficient conditions for the stationary density of semimartingale reflected Brownian motion in a wedge to be written as a finite sum of terms of exponential product form. Relyin...
Multifractional Brownian motion (mBm), denoted here by X, is one of the paradigmatic examples of a continuous Gaussian process whose pointwise H¨older exponent depends on the location. Recall that X...
The purpose of this work is to study some possible application of FKG inequality to the Brownian motion and to Stochastic Differential Equations. We introduce a special ordering on the Wiener space an...

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