118550208
A limit theorem of branching processes and continuous state branching processes
120055632
On discontinuous additive functionals and Lévy measures of a Markov process
118344939
Convergence of isotropic scattering transport process to Brownian motion
Introduction Let us consider transporting particle in the n-dimensional Euclidian space R. It is assumed that a particle originating at a point x^R moves in a straight line with constant speed c and continues to move until it suffers a collision. The probability that the particle has a collision between t and t + Δ is kΔ + o(Δ), where k is constant. When a particle has a collision, say at y in R, it moves afresh from y with an isotropic choice of direction independent of past history. It has been proved that, when c and k grows up indefinitely under the relation k\c = 2/n + 0(1), the distribution of a particle converges weakly to that of Brownian motion for the one-dimensional case by N. Ikeda and H. Nomoto [2] (cf. M.A. Pinsky [4]), and for the two-dimensional case by To. Watanabe [6] (cf. A.S. Monin [3]). The purpose of this paper is to show that the same result is also valid for the multi-dimensional case. In section 1, we shall define the n-dimensional transport process with speed c. In section 2, we investigate the resolvent and its Fourier transform. In section 3, using the result of section 2, we shall show that the distribution of transport process with speed c converges to that of the Brownian motion as c ̂ oo under the assumption: k\c = 2/n + 0(1) (Theorem 1). In section 4, we shall show that the transport process with speed c converges weakly to the Brownian motion, considering them as the measures on the space ^ of continuous functions.
116940448
Lectures on stochastic di erential equations and Malliavin calculus
118710372
On some relations between the harmonic measure and the Levy measure for a certain class of Markov processes.
116204420
Malliavin's calculus in terms of generalized Wiener functionals
46977756
A model of mind-body relation in terms of modular logic