PROBABILITIES OF ANALOGUE OF WIENER PATHS CROSSING CONTINUOUSLY DIFFERENTIABLE CURVES

• 발행기관: 충청수학회
• 저자명: Kun Sik Ryu
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 22, No. 3, 579~586쪽, 전체 8쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2009.09.30

영문 초록

Let be a complete probability measure on R, let m be the analogue of Wiener measure over paths on [0, T] and let f(t) be continuously differentiable on [0, T]. In this note, we give the analogue of Wiener measure m of {x in C[0, T]|x(0) < f(0) and x(s0)  f(s0) for some s0 in [0, T]} by use of integral equation techniques. This result is a generalization of Park and Paranjape’s 1974 result[1].

목차

1. Introduction

2. Statement of the result and proof

References