科研之友
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摘要
We study the martingale problem associated with the operator
Lu(s, x) = partial derivative(s)u(s, x) + 1/2 Sigma(d0)(i,j=1) a(ij)(s, x)partial derivative(ij)u(s, x) + Sigma(d)(i,j=1) B(ij)x(j)partial derivative(i)u(s, x),
where d(0) < d. We show that the martingale problem is well-posed when the function a is continuous and strictly positive definite on R-d0 and the matrix B takes a particular lower-diagonal, block form. We then localize this result to show that the martingale problem remains well-posed when B is replaced by a sufficiently smooth vector field whose Jacobian matrix satisfies a nondegeneracy condition.
- 出版日期2013-2
