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Moment Functions and Central Limit Theorem for Jacobi Hypergroups on [ $$0,\infty $$ [
Springer Science and Business Media LLC - Tập 27 - Trang 278-300 - 2012
In this paper, we derive sharp estimates and asymptotic results for moment functions on Jacobi type hypergroups. Moreover, we use these estimates to prove a central limit theorem (CLT) for random walks on Jacobi hypergroups with growing parameters
$$\alpha ,\beta \rightarrow \infty $$
. As a special case,...... hiện toàn bộ
The Central Limit Problem for Random Vectors with Symmetries
Springer Science and Business Media LLC - Tập 20 - Trang 697-720 - 2007
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein’s method of exchangeable pairs; as far as we kn...... hiện toàn bộ
A Kolmogorov–Chentsov Type Theorem on General Metric Spaces with Applications to Limit Theorems for Banach-Valued Processes
Springer Science and Business Media LLC - Tập 36 - Trang 1454-1486 - 2022
This paper deals with moduli of continuity for paths of random processes indexed by a general metric space
$$\Theta $$
with values in a general metric space
$${{\mathcal {X}}}$$
. Adapting the mome...... hiện toàn bộ
A Functional LIL for d-Dimensional Stable Processes; Invariance for Lévy- and Other Weakly Convergent Processes
Springer Science and Business Media LLC - - 2007
We establish a functional LIL for the maximal process M(t) :=sup 0≤s≤t
‖X(s)‖ of an ℝ
d
-valued α-stable Lévy process X, provided X(1) has density bounded away from zero over some neighborhood of the origin. We also provide a broad invariance result governing a class independent-increment processes related to the domain of attraction of X...... hiện toàn bộ
A Technique for Stochastic Control Problems with Unbounded Control Set
Springer Science and Business Media LLC - Tập 12 - Trang 255-270 - 1999
We describe a change of time technique for stochastic control problems with unbounded control set. We demonstrate the technique on a class of maximization problems that do not have optimal controls. Given such a problem, we introduce an extended problem which has the same value function as the original problem and for which there exist optimal controls that are expressible in simple terms. This de...... hiện toàn bộ
A Conditional CLT which Fails for Ergodic Components
Springer Science and Business Media LLC - Tập 21 - Trang 687-703 - 2007
We show that the conditional central limit theorem can take place for a stationary process defined on a nonergodic dynamical system while this last does not satisfy the central limit theorem for any ergodic component. There exists an ergodic Markov chain such that the conditional central limit theorem is satisfied for an invariant measure but fails to hold for almost all starting points.
Tail Probabilities of St. Petersburg Sums, Trimmed Sums, and Their Limit
Springer Science and Business Media LLC - Tập 30 - Trang 1104-1129 - 2016
We provide exact asymptotics for the tail probabilities
$${\mathbb {P}}\{ S_{n,r} > x \}$$
as
$$x \rightarrow \infty $$
...... hiện toàn bộ
Limiting Distributions for a Class of Super-Brownian Motions with Spatially Dependent Branching Mechanisms
Springer Science and Business Media LLC - - Trang 1-51 - 2023
In this paper, we consider a large class of super-Brownian motions in
$${\mathbb {R}}$$
with spatially dependent branching mechanisms. We establish the almost sure growth rate of the mass located outside a time-dependent interval
$$(-\delta t,\delt...... hiện toàn bộ
Law of the iterated logarithm for perturbed empirical distribution functions evaluated at a random point for nonstationary random variables
Springer Science and Business Media LLC - Tập 7 - Trang 831-855 - 1994
We consider perturbed empirical distribution functions
$$\hat F_n (x) = 1/n\sum\nolimits_{i = 1}^n {G_n (x - X_i )} $$
, where {Ginn, n≥1} is a sequence of continuous distribution functions converging weakly to the distribution function of unit mass at 0, and {Xi, i≥1} is a non-stationary sequence of abs...... hiện toàn bộ
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