학술저널
PROBABILITIES OF ANALOGUE OF WIENER PATHS CROSSING CONTINUOUSLY DIFFERENTIABLE CURVES
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 22, No. 3
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2009.09579 - 586 (8 pages)
- 0
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].
1. Introduction
2. Statement of the result and proof
References
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