A class of limit theorems for conditional distributions

Limit Theorems for Stationary Distributions

For every N > 1, let X,X, X, * * be a real-valued stationary process, and let AX = Xn Xn. Suppose that E(AXn XN)= O(FN) and var(AXN xN)= O(TN), where eN and 7N are positive null sequences. Limiting distributions of XN as N oc are obtained for the cases tN = e N and 7N = o(eN). These results are established by an extension of a method due to Moran. The theory is illustrated by a variety of appli...

Central Limit Theorems for Conditional Markov Chains

This paper studies Central Limit Theorems for real-valued functionals of Conditional Markov Chains. Using a classical result by Dobrushin (1956) for non-stationary Markov chains, a conditional Central Limit Theorem for fixed sequences of observations is established. The asymptotic variance can be estimated by resampling the latent states conditional on the observations. If the conditional means...

Conditional limit theorems for ordered random walks

In a recent paper of Eichelsbacher and König (2008) the model of ordered random walks has been considered. There it has been shown that, under certain moment conditions, one can construct a k-dimensional random walk conditioned to stay in a strict order at all times. Moreover, they have shown that the rescaled random walk converges to the Dyson Brownian motion. In the present paper we find the ...

Class of Limit Theorems for Singular Diffusions

Moment Convergence in Conditional Limit Theorems

SVANTE JANSON Abstract. Consider a sum ∑N 1 Yi of random variables conditioned on a given value of the sum ∑N 1 Xi of some other variables, where Xi and Yi are dependent but the pairs (Xi, Yi) form an i.i.d. sequence. We consider here the case when each Xi is discrete. We prove, for a triangular array ((Xni, Yni)) of such pairs satisfying certain conditions, both convergence of the distribution...