A Dubins type solution to the Skorokhod embedding problem

作者：Baker David M^*

来源：Statistics & Probability Letters, 2012, 82(6): 1054-1058.

DOI：10.1016/j.spl.2012.03.006

• Skorokhod embedding problem
• Quantization
• Stopping time
• Brownian motion

Dubins (1968) gave the first solution to the Skorokhod embedding problem (SEP) based solely on the underlying Brownian motion, and thus requiring no additional independent random variable. The Dubins solution to the SEP, can be expressed as tau := sup{tau(n)} with tau(n) = inf{t >= tau(n-1) : W-t is an element of support of mu(n)}. Since the measures mu(n) are defined recursively, in order to compute mu(n), each of mu(0), . . . , mu(n-1) must first be computed. In this note, we give a new solution to the SEP by showing how to construct a different sequence of measures {mu(n)}(n is an element of N). The advantage of this solution is that for any given n, the measure mu(n) can be constructed directly without prior computation of the measures mu(0), . . . , mu(n-1).

• 出版日期2012-6