This paper proves a functional limit theorem for Stigler's result on the heavily trimmed sums of i.i.d. random variables. The limiting process will be expressed as a functional of a Kiefer process and we shall also see that it is a Brownian motion if and only if asymptotic normality holds.

The first problem attacked in this paper is answering the question whether all 1/[alpha]-self-similar [alpha]-stable processes with stationary increments are [alpha]-stable motions. The answer is yes for [alpha] = 2, no for 1[less-than-or-equals, slant][alpha]2 and unknown for 0[alpha]1. We...

Convergence in law of solutions of SDE having jumps is discussed assuming suitable convergence of the coefficients under a situation where the point process approaches a Poisson point process. As an application the asymptotic behavior of certain stochastic processes such as storage processes and...

Itô's theory of excursion point processes is reviewed and the following topics are discussed: Application of the theory to one-dimensional diffusion processes on half-intervals satisfying Feller's boundary conditions, and its multi-dimensional extension, i.e., the application of the theory to...

This volume contains the contributions to a conference that is among the most important meetings in financial mathematics. Serving as a bridge between probabilists in Japan (called the Ito School and known for its highly sophisticated mathematics) and mathematical finance and financial...

Based around recent lectures given at the prestigious Ritsumeikan conference, the tutorial and expository articles contained in this volume are an essential guide for practitioners and graduates alike who use stochastic calculus in finance. Among the eminent contributors are Paul Malliavin and...