منابع مشابه
On a Uniform Random Walk Conditioned to Stay Positive
For arbitrary N, M ∈ N we consider the ’uniform random walk’ (Sn)n≥0 with step sizes −N,−N +1, . . . , 0, , . . . , M and S0 = a ∈ N, conditioned to stay positive. The conditional generating functions of S0, S1, S2, . . . are expressed in terms of the coefficients of the expansion of the function PN+M (x) n, where Pi(x) = 1+x+· · ·+xi (i ∈ N, n ∈ Z), in ascending powers of x or, for M = 1, usin...
متن کاملAn Invariance Principle for Random Walk Bridges Conditioned to Stay Positive
We prove an invariance principle for the bridge of a random walk conditioned to stay positive, when the random walk is in the domain of attraction of a stable law, both in the discrete and in the absolutely continuous setting. This includes as a special case the convergence under diffusive rescaling of random walk excursions toward the normalized Brownian excursion, for zero mean, finite varian...
متن کاملLocal Probabilities for Random Walks Conditioned to Stay Positive
Let S0 = 0, {Sn, n ≥ 1} be a random walk generated by a sequence of i.i.d. random variables X1, X2, ... and let τ = min{n ≥ 1 : Sn ≤ 0} and τ = min{n ≥ 1 : Sn > 0}. Assuming that the distribution of X1 belongs to the domain of attraction of an α-stable law we study the asymptotic behavior, as n → ∞, of the local probabilities P(τ = n) and the conditional local probabilities P(Sn ∈ [x, x+∆)|τ > ...
متن کاملLarge Deviation Results for Random Walks Conditioned to Stay Positive
LetX1, X2, ... denote independent, identically distributed random variables with common distribution F , and S the corresponding random walk with ρ := limn→∞ P (Sn > 0) and τ := inf{n ≥ 1 : Sn ≤ 0}. Under the assumption that X is in the domain of attraction of an α-stable law with αρ < 1, we find an estimate for P (Sn > x|τ > n) which holds uniformly as x/cn →∞, where cn denote the norming cons...
متن کاملInvariance principles for random walks conditioned to stay positive
Let {Sn} be a random walk in the domain of attraction of a stable law Y, i.e. there exists a sequence of positive real numbers (an) such that Sn/an converges in law to Y. Our main result is that the rescaled process (S⌊nt⌋/an, t ≥ 0), when conditioned to stay positive, converges in law (in the functional sense) towards the corresponding stable Lévy process conditioned to stay positive. Under so...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2003
ISSN: 0024-6107,1469-7750
DOI: 10.1112/s0024610702003708