Average persistence of random walks
نویسندگان
چکیده
منابع مشابه
Average persistence of random walks
– We study the first passage time properties of an integrated Brownian curve both in homogeneous and disordered environments. In a disordered medium we relate the scaling properties of this center-of-mass persistence of a random walker to the average persistence, the latter being the probability Ppr(t) that the expectation value 〈x(t)〉 of the walker’s position after time t has not returned to t...
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— We study the first passage time properties of an integrated Brownian curve both in homogeneous and disordered environments. In a disordered medium we relate the scaling properties of this center of mass persistence of a random walker to the average persistence, the latter being the probability P pr(t) that the expectation value 〈x(t)〉 of the walker’s position after time t has not returned to ...
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We introduce a new method for studying large scale properties of random walks. The new concepts of transience and recurrence on the average are compared with the ones introduced in [1] and with the usual ones; their relationships are analyzed and various examples are provided.
متن کاملConditional persistence of Gaussian random walks
Let {Xn}n≥1 be a sequence of i.i.d. standard Gaussian random variables, let Sn = ∑n i=1 Xi be the Gaussian random walk, and let Tn = ∑n i=1 Si be the integrated (or iterated) Gaussian random walk. In this paper we derive the following upper and lower bounds for the conditional persistence: P { max 1≤k≤n Tk ≤ 0 ∣∣∣ Tn = 0, Sn = 0} . n, P { max 1≤k≤2n Tk ≤ 0 ∣∣∣ T2n = 0, S2n = 0} & n−1/2 logn , f...
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We study how the Hurst exponent alpha depends on the fraction f of the total time t remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walker's position to undergo a transition ...
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ژورنال
عنوان ژورنال: Europhysics Letters (EPL)
سال: 1999
ISSN: 0295-5075,1286-4854
DOI: 10.1209/epl/i1999-00220-2