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Superprocess Approximation For a Spatially Homogeneous Branching Walk
Superprocess Branching Random Walk
2009/5/8
We present an alternative particle picture for super-stable motion. It is based on a non-local branching mechanism in discrete time and only trivial space motion.
Strong Laws and Summability for Sequences of $phi$-Mixing Random Variables in Banach Spaces
StrongLaws Summability
2009/5/8
In this note the almost sure convergence of stationary, $varphi$-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the ful...
Surface Stretching for Ornstein Uhlenbeck Velocity Fields
Diffusion Processes Lyapunov Exponent Stochastic Flows
2009/5/8
The present note deals with large time properties of the Lagrangian trajectories of a turbulent flow in R^2 and R^3. We assume that the flow is driven by an incompressible time-dependent random veloci...
Fractional Brownian Motion and the Markov Property
Gaussian processes Markov Processes Numerical Approximation Ergodic Theorem
2009/5/8
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This leads naturally to:
1. A...
Brownian Excursion Conditioned on Its Local Time
Brownian excursion continuum random tree Kingman's coalescent local time
2009/5/8
For a function $ell$ satisfying suitable integrability (but not continuity) requirements, we construct a process $(B^ell_u, 0 leq u leq 1)$ interpretable as Brownian excursion conditioned to have loca...
Weak Convergence of Reflected Brownian Motions
Brownian Motions Convergence mild technical assumptions
2009/5/8
We show that if a sequence of domains $D_k$ increases to a domain $D$ then the reflected Brownian motions in $D_k$'s converge to the reflected Brownian motion in $D$, under mild technical assumptions....
The Law of Large Numbers for U-statistics Under Absolute Regularity
Law of large numbers U-statistics absolute regularity
2009/5/8
We prove the law of large numbers for U-statistics whose underlying sequence of random variables satisfies an absolute regularity condition ($beta$-mixing condition) under suboptimal conditions.
On Uniqueness of a Solution of Lu=u^a with Given Trace
superdiffusion moderate solutions trace of a solution explosion points
2009/5/4
A boundary trace (G, m) of a solution of Delta u = u^a in a bounded smooth domain in R^d was first constructed by Le Gall who described all possible traces for a = 2, d= 2 in which case a solution is ...
Concentration of the Spectral Measure for Large Matrices
Random Matrices concentration inequalities non-commutative functionals
2009/5/4
We derive concentration inequalities for functions of the empirical measure of eigenvalues for large, random, self adjoint matrices, with not necessarily Gaussian entries. The results presented apply ...
A Converse Comparison Theorem for BSDEs and Related Properties of g-Expectation
backward stochastic differential equations comparison theorem
2009/5/4
In [1], Z. Chen proved that, if for each terminal condition $xi$, the solution of the BSDE associated to the standard parameter $(xi, g_1)$ is equal at time $t=0$ to the solution of the BSDE associate...
We provide a simple probabilistic proof of a result of J. Král and I. Netuka: If f is a measurable real-valued function on Rd (d> 1) then the set of points at which f has a strict fine local maxim...
A Characterization of the Set of Fixed Points of the Quicksort Transformation
Quicksort fixed point smoothing transformation domain of attraction coupling integral equation
2009/5/4
The limiting distribution m of the normalized number of key comparisons required by the Quicksort sorting algorithm is known to be the unique fixed point of a certain distributional transformation T -...
A Weak Law of Large Numbers for the Sample Covariance Matrix
Law of large numbers,affine normalization sample covariance domain of attraction generalized domain of attraction
2009/5/4
In this article we consider the sample covariance matrix formed from a sequence of independent and identically distributed random vectors from the generalized domain of attraction of the multivariate ...
We determine the law of the convex minorant $(M_s, sin [0,1])$ of a real-valued Cauchy process on the unit time interval, in terms of the gamma process. In particular, this enables us to deduce that t...
A Necessary and Sufficient Condition for the Lambda-Coalescent to Come Down from Infinity
coalescent Kochen-StoneLemma
2009/5/4
Let $Pi_{infty}$ be the standard $Lambda$-coalescent of Pitman, which is defined so that $Pi_{infty}(0)$ is the partition of the positive integers into singletons, and, if $Pi_n$ denotes the restricti...