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BOUNDS FOR KAC’S MASTER EQUATION
Markov chain the n ball random rotation selected at random
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2015/7/14
Mark Kac considered a Markov Chain on the n–sphere based on random rotations
in randomly chosen coordinate planes. This same walk was used by Hastings on
the orthogonal group. We show that the walk ...
Exponential and non-exponential upper bounds for the ruin probabilities for the double Cox processes risk models
Probability Double Cox processes Martingale method
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2011/11/4
In this paper, we consider a general insurance risk model in which the premium income process and the claim process are based on Cox processes. Exponential upper bounds for ruin probabilities are obta...
Upper bounds for the maximum of a random walk with negative drift
Limit theorems random walks renewal theorem
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2011/9/21
Abstract: Consider a random walk $S_n=\sum_{i=0}^n X_i$ with negative drift. This paper deals with upper bounds for the maximum $M=\max_{n\ge 1}S_n$ of this random walk in different settings of power ...
Fluctuation bounds in the exponential bricklayers process
Interacting particle systems universal fluctuation bounds second class particle convexity bricklayers process
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2011/9/20
Abstract: This paper is the continuation of our earlier paper, where we proved t^{1/3}-order of current fluctuations across the characteristics in a class of one dimensional interacting systems with o...
Uniform moment bounds of multi-dimensional functions of discrete-time stochastic processes
stochastic stability Markov chains uniform moment bounds invariant distributions stochastic control
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2011/9/20
Abstract: We establish conditions for uniform $r$-th moment bound of certain $\R^d$-valued functions of a discrete-time stochastic process taking values in a general metric space. The conditions inclu...
Explicit Bounds for the Distribution Function of the Sum of Dependent Normally Distributed Random Variables
Explicit Bounds Dependent Normally Distributed Random Variables Distribution Function of the Sum
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2011/9/19
Abstract: In this paper an analytic expression is given for the bounds of the distribution function of the sum of dependent normally distributed random variables. Using the theory of copulas and the i...
Upper Bounds for Markov Approximations of Ergodic Processes
Chains of infinite order coupling from the past algorithms canonical Markov approximation d-distance Kullback-Leibler divergence
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2011/9/19
Abstract: Chains of infinite order are generalizations of Markov chains that constitute a flexible class of models in the general theory of stochastic processes. These processes can be naturally studi...
Martingale Couplings and Bounds on the Tails of Probability Distributions
Martingale Couplings and Bounds Probability Distributions Statistics Theory
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2011/8/30
Abstract: Hoeffding has shown that tail bounds on the distribution for sampling from a finite population with replacement also apply to the corresponding cases of sampling without replacement. (A spec...