## JMI2010B-3 Scaling limit of d-inverse of Brownian motion with functional drift (pp.133-138)

Author(s)： Kouji Yano and Katsutoshi Yoshioka

J. Math-for-Ind. 2B (2010) 133-138.

Abstract
The d-inverse is a generalized notion of inverse of a stochastic process having a certain tendency of increasing expectations. Scaling limit of the d-inverse of Brownian motion with functional drift is studied. Except for degenerate case, the class of possible scaling limits is proved to consist of the d-inverses of Brownian motion without drift, one with explosion in finite time, and one with power drift.

Keyword(s).　 d-inverse, domain of attraction, Brownian motion with drift, geometric Brownian motion, option price, Black-Scholes formula