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CRITERIONS OF THE SlMILARITY FOR RANDOM WALKS AND BIRTH-AND-DEATH PROCESSES
Associated polynomials measures of orthogonality similar random walks
2009/9/18
This paper is devoted to study the similarity of birthand-
death processes with a discrete and continuous time. We discuss
some relations between the measures of orthogonality of the associated
pol...
CURSE OF DIMENSIONALITY IN APPROXIMATION OF RANDOM FIELDS
Random fields Gaussian processes fractional Brownian sheet linear approximation error
2009/9/18
Consider a random field of tensor product-type X (t),
~ E [ O l, l d, given by
where ( A ( ~ ) i , 0 ~ 1 2 , is an orthonormal system in L, KO, 11 and
(tklkENd are non-correlated random variables w...
CONVERGENCE RATE IN CLT FOR VECTOR-VALUED RANDOM FIELDS WITH SELF-N63RMALIZATIQ)N
Random fields dependence conditions CLT random matrix normalization convergence rate
2009/9/18
Statistical version of the central limit theorem (CLT)
with random matrix normalization is established for random fields
with valuea in a space Rk (k 3 1). Dependence structure of the field
under c...
ON THE RANDOM FUNCTIONAL CENTRAL LIMIT THEOREMS WITH ALMOST SURE CONVERGENCE
Almost sure central limit theorem functional random-sum central limit theorem lbgarithmic averages
2009/9/18
In this paper we present functional random-sum central
limit theorems with almost sure convergence for independent nonidentically
distributed random variables. We consider the case where
the summat...
A WARNING ABOUT AN INDEPENDENCE PROPERTY RELATED TO RANDOM BROVCTNIAN SCALING
Standard Brownian motion Brownian scaling excursion last zero first zero Brownian meander
2009/9/18
In this note, which develops a part of our paper [2], we
consider independence properties between Brownian motion, after
Brownian scaling on a random interval (a, b), and the length (b-a) of
the in...
ON TWE RENlARRABLE DISTRIBUTIONS OF MAXIPMA OF SOME FRAGMENTS OF THE STANI)ARD REFLECTING RANDOM WALK AND BROWNIAN MOTION
Standard random walk standard Brownian motion excursion meander comeander infinite divisibility
2009/9/18
In this paper, we consider some distributions of maxima
of excursions and related variables for standard random walk and
Brownian motion. We discuss the infinite divisibility properties of
these di...
ON THE STRONG LAW OF LARGE FOR SEQUENCES OF BLOCKWISE INDEPENDENT AND BLOCKWISE p-ORTNOGONA RANDOM ELEMENTS IN RADEMACWER TYPE p BANACW SPACES
Blockwise independent random elements blockwise p-orthogonal random elements almost sure convergence
2009/9/18
For a sequence of random elements {G, n 2 1) taking
values in a real separable Rademacher type p (1 < p < 2) Banach space
and positive constants b,l 7 co, conditions are provided for the strong
law...
LAWS OF LARGE NUMBERS FOR TWO TAILED PARETO RANDOM VARIABLES
Almost sure convergence weak law of large numbers strong law of large numbers
2009/9/18
We sample m random variables from a two tailed Pareto
distribution. A two tailed Pareto distribution is a random variable whose
right tail is px−2 and whose left tail is qx−2, where p + ...
DISCRETE APPROXIMATIONS OF REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH RANDOM TERMINAL TIME
Reflected backward stochastic differential equations random terminal time discrete approximation methods
2009/9/18
We study convergence of discrete approximations of reflected
backward stochastic differential equations with random terminal
time in a general convex domain. Applications to investigation of the via...
ASSOCIATION CRITERIA FOR M-INFINITELY-DIVISIBLE AND U-INFINITELY-DIVISIBLE RANDOM SETS
Association infinite association M-infinitedivisibility U-infinite-divisibility
2009/9/18
We study random convex compact sets infinitely divisible
with respect to the Minkowski addition and establish a sufficient condition
for their association as well as a necessary and sufficient condi...
MAXIMAL INEQUALITIES FOR U-PROCESSES OF STRONGLY MIXING RANDOM VARIABLES
Besov space Hoeffding decomposition stochastic equicontinuity strong mixing U-process.
2009/9/18
Maximal inequalities for U-processes are required in order
to achieve a reduction to the first nonvanishing term in their Hoeffding’s
decomposition, which is the relevant quantity for statistical in...
A Note on the Product of Normal and Laplace Random Variables
A Note the Product of Normal Laplace Random Variables
2009/9/17
A Note on the Product of Normal and Laplace Random Variables。
On the Values of Optimal Stopping Problems for Generalized Averages of Discrete Random Variables
Optimal Stopping Problems Generalized Averages Discrete Random Variables
2009/9/17
On the Values of Optimal Stopping Problems for Generalized Averages of Discrete Random Variables。
In this paper, we develop a general theory on the coverage probability of random inter-
vals defined in terms of discrete random variables with continuous parameter spaces. The
theory shows that the...
On the scaling limit of simple random walk excursion measure in the plane
Brownian excursion measure Brownian motion simple random walk excursion measure excursion Poisson kernel strong approximation scaling limit
2009/6/12
The Brownian excursion measure is a conformally invariant innite measure on curves. It gured prominently in one of rst major applications of SLE, namely the explicit calculations of the planar Brownia...