TITLE

Limit theorems of continuous-time random walks with tails

AUTHOR(S)
Li, Yuqiang
PUB. DATE
April 2013
SOURCE
Frontiers of Mathematics in China;Apr2013, Vol. 8 Issue 2, p371
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We study the functional limits of continuous-time random walks (CTRWs) with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an α-stable Lévy process in D([0, 1]) with M-topology but the corresponding scaled CTRWs converge weakly to the same limit in D([0, 1]) with J-topology.
ACCESSION #
86406841

 

Related Articles

  • Limit theorems for random walks under irregular conductance. FUKASAWA, Masaaki // Proceedings of the Japan Academy, Series A: Mathematical Science;Oct2013, Vol. 89 Issue 8, p87 

    For a general one-dimensional random walk with state-dependent transition probabilities, we present weak limits of the empirical moments of conductance along the path of the random walk. In particular we obtain remarkably simple quenched convergences under random conductance model.

  • LIMIT THEOREMS FOR A GENERALIZED FELLER GAME. KEISUKE MATSUMOTO; TOSHIO NAKATA // Journal of Applied Probability;Mar2013, Vol. 50 Issue 1, p54 

    In this paper we study limit theorems for the Feller game which is constructed from one-dimensional simple symmetric random walks, and corresponds to the St. Petersburg game. Motivated by a generalization of the St. Petersburg game which was investigated by Gut (2010), we generalize the Feller...

  • Convergence of nonhomogeneous random walks generated by compound Cox processes to generalized variance-gamma Lévy processes. Korolev, V.; Korchagin, A.; Zeifman, A. // Doklady Mathematics;Jul2015, Vol. 92 Issue 1, p408 

    Functional limit theorems on the convergence of nonhomogeneous random walks generated by compound Cox processes to Lévy processes with generalized one-dimensional variance-gamma distributions, in particular, to subordinate Wiener processes with subordinator being a Lévy-Weibull process,...

  • CONDITIONAL LIMIT THEOREMS FOR THE TERMS OF A RANDOM WALK REVISITED. BAR-LEV, SHAUL K.; SCHULTE-GEERS, ERNST; STADJE, WOLFGANG // Journal of Applied Probability;Sep2013, Vol. 50 Issue 3, p871 

    In this paper we derive limit theorems for the conditional distribution of X1 given Sn = Sn as n → ∞, where the Xi are independent and identically distributed (i.i.d.) random variables, Sn = X1 + ··· + Xn, and sn/n converges or sn ≡ s is constant. We obtain convergence...

  • One-sided local large deviation and renewal theorems in the case of infinite mean. Doney, R. A. // Probability Theory & Related Fields;1997, Vol. 107 Issue 4, p451 

    Summary. If {S[sub n] ,n?0} is an integer-valued random walk such that S[sub n] /a[sub n] converges in distribution to a stable law of index a? (0,1) as n? 8, then Gnedenko�s local limit theorem provides a useful estimate for P{S[sub n] =r} for values of r such that r/a[sub n] is bounded....

  • Semicontinuous limits of nets of continuous functions. Beer, Gerald // Mathematical Programming;Jun2013, Vol. 139 Issue 1/2, p71 

    In this paper we present a topology on the space of real-valued functions defined on a functionally Hausdorff space $$X$$ that is finer than the topology of pointwise convergence and for which (1) the closure of the set of continuous functions $$\mathcal{C }(X)$$ is the set of upper...

  • The Γ-Limit of the Two-Dimensional Ohta—Kawasaki Energy. I. Droplet Density. Goldman, Dorian; Muratov, Cyrill B.; Serfaty, Sylvia // Archive for Rational Mechanics & Analysis;Nov2013, Vol. 210 Issue 2, p581 

    This is the first in a series of two papers in which we derive a Γ-expansion for a two-dimensional non-local Ginzburg–Landau energy with Coulomb repulsion, also known as the Ohta–Kawasaki model, in connection with diblock copolymer systems. In that model, two phases appear,...

  • Weak convergence of partial maxima processes in the M topology. Krizmanić, Danijel // Extremes;Sep2014, Vol. 17 Issue 3, p447 

    It is known that for a sequence of independent and identically distributed random variables ( X) the regular variation condition is equivalent to weak convergence of partial maxima $M_{n}= \max \{X_{1}, \ldots , X_{n}\}$, appropriately scaled. A functional version of this is known to be true as...

  • The continuum limit of critical random graphs. Addario-Berry, L.; Broutin, N.; Goldschmidt, C. // Probability Theory & Related Fields;Apr2012, Vol. 152 Issue 3/4, p367 

    We consider the Erdős-Rényi random graph G( n, p) inside the critical window, that is when p = 1/ n + λ n, for some fixed $${\lambda \in \mathbb{R}}$$ . We prove that the sequence of connected components of G( n, p), considered as metric spaces using the graph distance rescaled by n,...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics