We derive a perturbation expansion for general interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the true (weakly) self-avoiding walk and loop-erased random walk. We use the expansion to prove a law of large numbers and central limit theorem for two models: (i) ...

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

In this paper we develop a model for random walk-based search mechanisms in unstructured P2P networks. This model is used to obtain analytical expressions for the performance metrics of random walk search in terms of the popularity of the resource being searched for and the random walk parameters. We propose an equation-based adaptive search mechanism that uses an estimate of the popularity of ...

The paper is a practical application of the random walk model on stock price behaviour. The academic literature has moved beyond this random walk approach and the recent focus is now much more on how to improve the forecasts. Since the performance of the random walk model has been contextual, it is desirable that the model is tested in different contexts. Our model shows good results in the Ind...

‎we investigate two constructions‎ - ‎the replacement and the zig-zag‎ ‎product of graphs‎ - ‎describing several fascinating connections‎ ‎with combinatorics‎, ‎via the notion of expander graph‎, ‎group‎ ‎theory‎, ‎via the notion of semidirect product and cayley graph‎, ‎and‎ ‎with markov chains‎, ‎via the lamplighter random walk‎. ‎many examples‎ ‎are provided‎.

In this paper we investigate the merits of artiicial neural networks in forecasting foreign exchange rates. From previous research it is known that it is hard to beat the random walk model using structural exchange rate models. In this paper we show that by using a suitable multivariate speciication a structural model can be derived that beats the random walk. By introducing a new method for mu...