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![Figure 1: The set S on [0, 0.5].](https://thumb-ap.123doks.com/thumbv2/123dok/979936.915765/10.595.117.451.153.249/figure-the-set-s-on.webp)
![Figure 3: The set S(3) on [0, 0.5]2 × [0, 0.3].](https://thumb-ap.123doks.com/thumbv2/123dok/979936.915765/16.595.196.402.156.308/figure-the-set-s-on.webp)
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The behaviour of the horizontal projection of the random walk is less obvious: in Sections 3, 4 and 5 we prove that the expected values of the horizontal distance, of its
We demonstrate this approach in two ways: we use it to prove that a polynomial approximation exists, reproducing the results of [FU96, U98] in the case the random walk is bounded
We prove that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean.. We show that
Indeed, using estimates for the so-called tan points of the simple random walk, introduced in [1] and subse- quently used in [7, 8], it is possible to prove that, when d ≥ 2, the
We prove the existence and uniqueness of a strong solution of a stochastic differential equation with normal reflection representing the random motion of finitely many globules..
One example of such a set that is not connected is the path of a non-nearest neighbor random walk whose increments have finite range; a possible application of our result would be
Recently, in [MR07c], we have shown that the edge-reinforced random walk on any locally finite graph has the same distribution as a random walk in a random environment given by
To prove this theorem we extend the bounds proved in [ 2 ] for the continuous time simple random walk on (Γ , µ ) to the slightly more general random walks X and Y defined
