Harmonic Analysis of Stochastic Equations and Backward Stochastic Differential Equations

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dc.creatorDelbaen, Freddy
dc.creatorTang, Shanjian
dc.date2008-01-23
dc.date.accessioned2026-07-07T08:56:02Z
dc.date.available2026-07-07T08:56:02Z
dc.descriptionThe BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) in $\cR^p$ ($p\in [1, \infty)$) and backward stochastic differential equations (BSDEs) in $\cR^p\times \cH^p$ ($p\in (1, \infty)$) and in $\cR^\infty\times \bar{\cH^\infty}^{BMO}$, with the coefficients being allowed to be unbounded. In particular, the probabilistic version of Fefferman's inequality plays a crucial role in the development of our theory, which seems to be new. Several new results are consequently obtained. The particular multi-dimensional linear case for SDEs and BSDEs are separately investigated, and the existence and uniqueness of a solution is connected to the property that the elementary solutions-matrix for the associated homogeneous SDE satisfies the reverse Hölder inequality for some suitable exponent $p\ge 1$. Finally, we establish some relations between Kazamaki's quadratic critical exponent $b(M)$ of a BMO martingale $M$ and the spectral radius of the solution operator for the $M$-driven SDE, which lead to a characterization of Kazamaki's quadratic critical exponent of BMO martingales being infinite.
dc.description40 pages
dc.identifierhttps://arxiv.org/abs/0801.3505
dc.identifierhttp://arxiv.org/abs/0801.3505
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146469
dc.subjectProbability
dc.subjectFunctional Analysis
dc.subject60H10,60H20,60H99,60G44,60G46
dc.titleHarmonic Analysis of Stochastic Equations and Backward Stochastic Differential Equations
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