On a Directionally Reinforced Random Walk
نویسندگان
چکیده
We consider a generalized version of a directionally reinforced random walk, which was originally introduced by Mauldin, Monticino, and von Weizsäcker in [20]. Our main result is a stable limit theorem for the position of the random walk in higher dimensions. This extends a result of Horváth and Shao [13] that was previously obtained in dimension one only (however, in a more stringent functional form).
منابع مشابه
Directionally Reinforced Random Walks
This paper introduces and analyzes a class of directionally reinforced random walks The work is motivated by an elementary model for time and space correlations in ocean surface wave elds We develop some basic properties of these walks For instance we investigate recurrence properties and give conditions under which the limiting continuous versions of the walks are Gaussian di usion processes M...
متن کاملLevel Crossing Probabilities Ii: Polygonal Recurrence of Multidimensional Random Walks
In part I (math.PR/0406392) we proved for an arbitrary onedimensional random walk with independent increments that the probability of crossing a level at a given time n is O(n). In higher dimensions we call a random walk ’polygonally recurrent’ (resp. transient) if a.s. infinitely many (resp. finitely many) of the straight lines between two consecutive sites hit a given bounded set. The above e...
متن کاملAn expansion for self-interacting random walks
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) ...
متن کاملReinforced Random Walk
This thesis aim is to present results on a stochastic model called reinforced random walk. This process was conceived in the late 1980’s by Coppersmith and Diaconis and can be regarded as a generalization of a random walk on a weighted graph. These reinforced walks have non-homogeneous transition probabilities, which arise from an interaction between the process and the weights. We survey artic...
متن کاملExcited Random Walk in Three Dimensions Has Positive Speed
Excited random walk is a model of a random walk on Z which, whenever it encounters a new vertex it receives a push toward a specific direction, call it the “right”, while when it reaches a vertex it “already knows”, it performs a simple random walk. This model has been suggested in [BW] and had since got lots of attention, see [V, Z]. The reason for the interest is that it is situated very natu...
متن کامل