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- W3124804511 abstract "Consider two laws $P$ and $Q$ of multidimensional possibly explosive diffusions with common diffusion coefficient $mathfrak {a}$ and drift coefficients $mathfrak {b}$ and $mathfrak {b}+ mathfrak {a}mathfrak {c}$, respectively, and the law $P^{circ }$ of an auxiliary diffusion with diffusion coefficient $langle mathfrak {c}, mathfrak {a}mathfrak {c}rangle ^{-1}mathfrak {a}$ and drift coefficient $langle mathfrak {c}, mathfrak {a}mathfrak {c}rangle ^{-1}mathfrak {b}$. We show that $P ll Q$ if and only if the auxiliary diffusion $P^{circ }$ explodes almost surely and that $Pperp Q$ if and only if the auxiliary diffusion $P^{circ }$ almost surely does not explode. As applications we derive a Khasminskii-type integral test for absolute continuity and singularity, an integral test for explosion of time-changed Brownian motion, and we discuss applications to mathematical finance." @default.
- W3124804511 created "2021-02-01" @default.
- W3124804511 creator A5036764370 @default.
- W3124804511 date "2021-01-01" @default.
- W3124804511 modified "2023-09-23" @default.
- W3124804511 title "On absolute continuity and singularity of multidimensional diffusions" @default.
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- W3124804511 doi "https://doi.org/10.1214/20-ejp555" @default.
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