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7 matches found
XV: 40, 590-603, LNM 850 (1981)
STROOCK, Daniel W.; YOR, Marc
Some remarkable martingales (Martingale theory)
This is a sequel to a well-known paper by the authors (Ann. ENS, 13, 1980) on the subject of pure martingales. A continuous martingale $(M_t)$ with $<M,M>_{\infty}=\infty$ is pure if the time change which reduces it to a Brownian motion $(B_t)$ entails no loss of information, i.e., if $M$ is measurable w.r.t. the $\sigma$-field generated by $B$. The first part shows the purity of certain stochastic integrals. Among the striking examples considered, the stochastic integrals $\int_0^t B^n_sdB_s$ are extremal for every integer $n$, pure for $n$ odd, but nothing is known for $n$ even. A beautiful result unrelated to purity is the following: complex Brownian motion $Z_t$ starting at $z_0$ and its (Lévy) area integral generate the same filtration if and only if $z_0\neq0$
Keywords: Pure martingales, Previsible representation
Nature: Original
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XVII: 23, 205-220, LNM 986 (1983)
CHEN, Mu-Fa; STROOCK, Daniel W.
$\lambda_\pi$-invariant measures
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XX: 21, 341-348, LNM 1204 (1986)
CARLEN, Eric A.; STROOCK, Daniel W.
An application of the Bakry-Émery criterion to infinite dimensional diffusions
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XXI: 01, 1-7, LNM 1247 (1987)
STROOCK, Daniel W.
Homogeneous chaos revisited
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XXI: 34, 574-578, LNM 1247 (1987)
DUDLEY, Richard M.; STROOCK, Daniel W.
Slepian's inequality and commuting semigroups
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XXII: 28, 316-347, LNM 1321 (1988)
STROOCK, Daniel W.
Diffusion semigroups corresponding to uniformly elliptic divergence form operators
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XXXVII: 18, 399-414, LNM 1832 (2003)
ROSU, Ioanid; STROOCK, Daniel W.
On the derivation of the Black--Scholes formula