On the approximation of stochastic differential equation and on Stroock- Varadhan's support theorem
The celebrated Stroock-Varadhan's support theorem for diffusions is extended to the following case: \(x_ t\) is a solution of the stochastic differential equation \[ dx_ t=b(t,x_ t)dt+\sum^{l}_{i=1}\sigma_ i(t,x_ t)\circ dm^ i_ t, \] where \(m_ t\) is a continuous semimartingale, b and \(\sigma\) are supposed to be unbounded, Lipschitz continuous and with at most linear growth. Under additional technical assumptions, the author gives the complete description of the support of the law of \(x_ t\).
Stroock-Varadhan's support theorem for diffusions
scientific article; zbMATH DE number 4169779