Search

Let ζ be a Markov chain on a finite state space D, f a function from D to ℝd, and Sn = ∑k=1nf(ζk). We prove an invariance theorem for S and derive an explicit expression of the limit covariance matrix. We give its exact value for p-reinforced random walks on ℤ2 with p = 1, 2, 3.

Correlated random walk models figure prominently in many scientific disciplines. Of fundamental importance in such applications is the development of the characteristic function of the n-step probability distribution since it contains complete information on the probability structure of the process. Using a simple algebraic lemma we derive the n-step characteristic function of the Gillis correlated random walk together with other related results. In particular, we present a new and simple proof of Gillis's conjecture, consider the generalization to the Gillis–Domb–Fisher walk, and examine the effect of including an arbitrary initial distribution.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

Un principe d'invariance pour une classe de marches p-corrélées sur ℤd

The Gillis–Domb–Fisher correlated random walk

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

Un principe d'invariance pour une classe de marches p-corrélées sur ℤd

The Gillis–Domb–Fisher correlated random walk