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Asymptotic Analysis of a Random Walk on a Hypercube with Many Dimensions。
Under natural assumptions a Feller type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, pos...
Abstract: Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci, a new framework based on asymptotic series has recently...
Abstract: Let $X$ be a real valued L\'evy process that is in the domain of attraction of a stable law without centering with norming function $c.$ As an analogue of the random walk results in \cite{vw...
Abstract: We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome bu...
Abstract: This paper resolves a question proposed in Kardaras and Robertson (2011): how to invest in a robust growth-optimal way in a market where precise knowledge of the covariance structure of the ...
Abstract: We derive the asymptotic distribution of the total length $L_n$ of a Beta($2-\alpha,\alpha$)-coalescent tree for $1<\alpha < 2$, starting from $n$ individuals. There are two regimes: If $\al...
Abstract: In this paper we consider first-passage percolation on certain subgraphs of the $\Z^d$ nearest neighbour graph. We present a three-fold extension of the Shape Theorem. Firstly, we show that ...
Abstract: We prove the existence of a 1/N expansion to all orders in beta matrix models with a confining, off-critical potential corresponding to an equilibrium measure with a connected support. Thus,...
The standard Bayesian Information Criterion (BIC) is derived under regularity conditions which are not always satis ed by the graphical models with hidden variables.
We extend a recent analysis of synchronization for exact finite-state sources to nonexact sources for which synchronization occurs only asymptotically. Although the asymptotic case requires more sophi...
In this study, the semi-Markovian random walk with a special barrier (X(t)) is considered and under some weak assumptions the ergodicity of this process is discussed. Moreover, the characteristic func...

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