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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
Key words: asymptotic formula, Green function, random walk of zero mean and finite variances, absorption on a line.. AMS 2000 Subject Classification: Primary 60G50;
Keywords: Gaussian random walk; maximum; Riemann zeta function; Euler-Maclaurin summa- tion; equidistant sampling of Brownian motion; finite
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
Then, we give sufficient conditions for a σ-finite measure to be invariant for this conditional process with any realization of the given Brownian motion.. In Section 4, we show
The case of Markov chains was first considered by Marton [20; 21] : for uniformly contracting Markov chains, in particular for ergodic Markov chains with finite state space,
There it has been shown that, under certain moment conditions, one can construct a k -dimensional random walk conditioned to stay in a strict order at all times.. Moreover, they
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
