Given two stochastic equations with different drift terms, under very weak assumptions Liptser and Shiryaev provide the absolute continuity of the law of the solution of one equation with respect to the other one by means of Girsanov transform; then they consider the equivalence of these laws. Their assumptions iinvolve both the drift terms. We are interested in the same results but with the main assumption involving only the difference of the drift terms. Applications of our result will be presented in the finite as well as in the infinite-dimensional setting.
A note on a result of Liptser-Shiryaev
FERRARIO, BENEDETTA
2012-01-01
Abstract
Given two stochastic equations with different drift terms, under very weak assumptions Liptser and Shiryaev provide the absolute continuity of the law of the solution of one equation with respect to the other one by means of Girsanov transform; then they consider the equivalence of these laws. Their assumptions iinvolve both the drift terms. We are interested in the same results but with the main assumption involving only the difference of the drift terms. Applications of our result will be presented in the finite as well as in the infinite-dimensional setting.File in questo prodotto:
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