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Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems
stationary solutions multivariate stochastic recursions related limit theorems
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2010/11/12
Let $\Phi_n$ be an i.i.d. sequence of Lipschitz mappings of $\R^d$. We study the Markov chain $\{X_n^x\}_{n=0}^\8$ on $\R^d$ defined by the recursion $X_n^x = \Phi_n(X^x_{n-1})$, $n\ge 0$, $X_0=x\in\...
A probabilistic approach to local limit theorems with applications to random graphs
local limit theorems applications to random graphs
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2010/11/19
In this article, we develop a general method to obtain local limit theorems from distributional limit theorems. Our results use probabilistic arguments and yield explicit bounds on the quality of app...