Uniqueness of the embedding continuous convolution semigroup of a Gaussian probability measure on the affine group and an application in mathematical finance

作者：Neuenschwander Daniel^*

来源：Monatshefte fur Mathematik, 2013, 171(1): 91-101.

DOI：10.1007/s00605-013-0490-5

• Continuous convolution semigroups of probability measures
• Affine group
• Levy processes
• Brownian motion

Let {mu((i))(t)}(t %26gt;= 0) (i = 1, 2) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that mu((1))(1) = mu((2))(1). Assume furthermore that {mu((1))(t)}(t %26gt;= 0) is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then mu((1))(1) = mu((2))(1) for all t %26gt;= 0. We end up with a possible application in mathematical finance.

• 出版日期2013-7