Zobrazeno 1 - 10
of 98
pro vyhledávání: '"Uchiyama, Kôhei"'
Autor:
Uchiyama, Kohei
Let $F$ be a distribution function on the integer lattice $\mathbb{Z}$ and $S=(S_n)$ the random walk with step distribution $F$. Suppose $S$ is oscillatory and denote by $U_{\rm a}(x)$ and $u_{\rm a}(x)$ the renewal function and sequence, respectivel
Externí odkaz:
http://arxiv.org/abs/2102.04102
Autor:
Uchiyama, Kohei
Let $F\{dx\}$ be a relatively stable probability distribution on the whole real line and $S_n$ the random walk started at the origin with step distribution $F$. We obtain an exact asymptotic form of the Green measure $U\{x+dy\}= \sum_{n=0}^\infty P[S
Externí odkaz:
http://arxiv.org/abs/1911.10889
Autor:
Uchiyama, Kohei
Let $S=(S_n)$ be an oscillatory random walk on the integer lattice $\mathbb{Z}$ with i.i.d. increments. Let $V_{{\rm d}}(x)$ be the renewal function of the strictly descending ladder height process for $S$. We obtain several sufficient conditions --
Externí odkaz:
http://arxiv.org/abs/1908.00303
Autor:
Uchiyama, Kohei
This paper concerns a scaling limit of a one-dimensional random walk $S^x_n$ started from $x$ on the integer lattice conditioned to avoid a non-empty finite set $A$, the random walk being assumed to be irreducible and have zero mean. Suppose the vari
Externí odkaz:
http://arxiv.org/abs/1905.01120
Autor:
Uchiyama, Kohei
Publikováno v:
Stochastic processes and their Applications (2019), https://doi.org/10.1016/j.spa.2019.02.006
For a random walk on the integer lattice $\mathbb{Z}$ that is attracted to a strictly stable process with index $\alpha\in (1, 2)$ we obtain the asymptotic form of the transition probability for the walk killed when it hits a finite set. The asymptot
Externí odkaz:
http://arxiv.org/abs/1901.05568
Autor:
Uchiyama, Kohei
In this paper we consider an irreducible random walk on the integer lattice $\mathbb{Z}$ that is in the domain of normal attraction of a strictly stable process with index $\alpha\in (1, 2)$ and obtain the asymptotic form of the distribution of the h
Externí odkaz:
http://arxiv.org/abs/1808.01484
Autor:
Uchiyama, Kohei
Publikováno v:
Electronic Journal of Probability, vol. 25 (2020), article no. 153, 1-24
We consider a recurrent random walk of i.i.d. increments on the one-dimensional integer lattice and obtain a formula relating the hitting distribution of a half-line with the potential function, $a(x)$, of the random walk. Applying it, we derive an a
Externí odkaz:
http://arxiv.org/abs/1805.03971
Autor:
Uchiyama, Kohei
Let $S_n =X_1+\cdots +X_n$ be an irreducible random walk (r.w.) on the one dimensional integer lattice with zero mean, infinite variance and i.i.d. increments $X_n$. We obtain an upper and lower bounds of the potential function, $a(x)$, of $S_n$ in t
Externí odkaz:
http://arxiv.org/abs/1802.09832
Autor:
Uchiyama, Kohei
This paper concerns a random walk on a planar graph and presents certain estimates concerning the harmonic measures for the walk in a grid domain which estimates are useful for showing the convergence of a LERW (loop-erased random walk) to an SLE (st
Externí odkaz:
http://arxiv.org/abs/1705.03224