scholarly journals A functional limit theorem for stochastic integrals driven by a time-changed symmetricα-stable Lévy process

2014 ◽  
Vol 124 (1) ◽  
pp. 385-410 ◽  
Author(s):  
Enrico Scalas ◽  
Noèlia Viles
Keyword(s):  
Limit Theorem ◽  
Lévy Process ◽  
Functional Limit Theorem ◽  
Levy Process ◽  
Stochastic Integrals ◽  
Functional Limit ◽  
Stable Lévy Process

scholarly journals Path to survival for the critical branching processes in a random environment

2017 ◽  
Vol 54 (2) ◽  
pp. 588-602 ◽  
Author(s):  
Vladimir Vatutin ◽  
Elena Dyakonova
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Random Environment ◽  
Branching Process ◽  
Branching Processes ◽  
Functional Limit Theorem ◽  
Levy Process ◽  
Initial Part ◽  
Functional Limit ◽  
Critical Branching Process

Abstract A critical branching process {Zk, k = 0, 1, 2, ...} in a random environment is considered. A conditional functional limit theorem for the properly scaled process {log Zpu, 0 ≤ u < ∞} is established under the assumptions that Zn > 0 and p ≪ n. It is shown that the limiting process is a Lévy process conditioned to stay nonnegative. The proof of this result is based on a limit theorem describing the distribution of the initial part of the trajectories of a driftless random walk conditioned to stay nonnegative.

Convergence to the local time of Brownian meander

2019 ◽  
Vol 29 (3) ◽  
pp. 149-158 ◽  
Author(s):  
Valeriy. I. Afanasyev
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Local Time ◽  
Random Processes ◽  
Functional Limit Theorem ◽  
Zero Drift ◽  
Functional Limit ◽  
Brownian Meander

Abstract Let {Sn, n ≥ 0} be integer-valued random walk with zero drift and variance σ2. Let ξ(k, n) be number of t ∈ {1, …, n} such that S(t) = k. For the sequence of random processes $\begin{array}{} \xi(\lfloor u\sigma \sqrt{n}\rfloor,n) \end{array}$ considered under conditions S1 > 0, …, Sn > 0 a functional limit theorem on the convergence to the local time of Brownian meander is proved.

A conditioned functional limit theorem

1980 ◽  
Vol 12 (2) ◽  
pp. 296-297
Author(s):  
Wim Vervaat ◽  
J. C. Smit
Keyword(s):  
Limit Theorem ◽  
Functional Limit Theorem ◽  
Functional Limit
Sign in / Sign up

Export Citation Format

Share Document