On a directionally reinforced random walk

On a Directionally Reinforced Random Walk

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 functiona...

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...

Reinforced 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...

Vertex-reinforced Random Walk

This paper considers a class of non-Markovian discrete-time random processes on a finite state space {1, . . . , d}. The transition probabilities at each time are influenced by the number of times each state has been visited and by a fixed a priori likelihood matrix, R, which is real, symmetric and nonnegative. Let Si(n) keep track of the number of visits to state i up to time n, and form the f...

Vertex-Reinforced Random Walk on Arbitrary Graphs