7 citations · 22 across the 17 of their papers we have counts for
19 papers
The two-sided exit problem for a random walk on and having infinite variance II
Kohei Uchiyama
Let be a distribution function on the integer lattice and the random walk with step distribution . Suppose is oscillatory and denote by $U_{\rm a}…
A renewal theorem for relatively stable variables
Kohei Uchiyama
Let be a relatively stable probability distribution on the whole real line and the random walk started at the origin with step distribution . We obtain an exact…
The two-sided exit problem for a random walk on with infinite variance I
Kohei Uchiyama
Let be an oscillatory random walk on the integer lattice with i.i.d. increments. Let be the renewal function of the strictly descending ladder…
Scaling limits of random walk bridges conditioned to avoid a finite set
Kohei Uchiyama
This paper concerns a scaling limit of a one-dimensional random walk started from on the integer lattice conditioned to avoid a non-empty finite set , the random wal…
Asymptotically stable random walks of index killed on a finite set
Kohei Uchiyama
For a random walk on the integer lattice that is attracted to a strictly stable process with index we obtain the asymptotic form of the transition probab…
Recurrent random walks on with infinite variance: transition probabilities of them killed on a finite set
Kohei Uchiyama
In this paper we consider an irreducible random walk on the integer lattice that is in the domain of normal attraction of a strictly stable process with index $α\in (1…
The potential function and ladder variables of a recurrent random walk on with infinite variance
Kohei Uchiyama
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 poten…
Estimates of Potential functions of random walks on with zero mean and infinite variance and their applications
Kohei Uchiyama
Let be an irreducible random walk (r.w.) on the one dimensional integer lattice with zero mean, infinite variance and i.i.d. increments . We obtain an u…
Boundary behaviour of RW's on planar graphs and convergence of LERW to chordal SLE
Kohei Uchiyama
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 sho…
Asymptotic behaviour of a random walk killed on a finite set
Kohei Uchiyama
We study asymptotic behavior, for large time , of the transition probability of a two-dimensional random walk killed when entering into a non-empty finite subset . We show th…
The transition density of Brownian motion killed on a bounded set
Kohei Uchiyama
We study the transition density of a standard two-dimensional Brownian motion killed when hitting a bounded Borel set . We derive the asymptotic form of the density, say $p^A_t(…
One dimensional random walk killed on a finite set
Kohei Uchiyama
We study the transition probability, say , of a one-dimensional random walk on the integer lattice killed when entering into a non-empty finite set . The random walk…
Brownian hitting distributions in space-time of bounded sets and the expected volume of Wiener sausage for Brownian bridges
Kohei Uchiyama
The space-time distribution, say, of Brownian hitting of a bounded Borel set of the -dimensional Euclidian space is studied. We derive the asymptotic form of…
Density of space-time distribution of Brownian first hitting of a disc and a ball
Kohei Uchiyama
We compute the joint distribution of the site and the time at which a -dimensional standard Brownian motion hits the surface of the ball for the f…
The expected area of the Wiener sausage swept by a disc
Kohei Uchiyama
The expected areas of the Wiener sausages swept by a disc attached to the two-dimensional Brownian Bridge joining the origin to a point x over a time interval [0,t] are computed. I…
Asymptotics of the densities of the first passage time distributions for Bessel diffusions
Kohei Uchiyama
This paper concerns the first passage times of Bessel processes to a point on the positive real line. We are interested in the case when the process starts at a position on its rig…
The hitting distribution of a line segment for two dimensional random walks
Kôhei Uchiyama
Asymptotic estimates of the hitting distribution of a long segment on the real axis for two dimensional random walks on of zero mean and finite variances are obtained:…
One dimensional lattice random walks with absorption at a point / on a half line
Kohei Uchiyama
This paper concerns a random walk that moves on the integer lattice and has zero mean and a finite variance. We obtain first an asymptotic estimate of the transition probability of…
Asymptotic estimates of the distribution of Brownian hitting time of a disc
Kohei Uchiyama
The distribution of the first hitting time of a disc for the standard two dimensional Brownian motion is computed. By investigating the inversion integral of its Laplace transform…