Large deviations and support theorem for diffusion processes via rough paths

By Michel Ledoux, Zhongmin Qian, Tusheng Zhang. 2002

118 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e02fce06df7aba668d62b87de7cecb07b19ab28e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Mathematical Physics

Citations in the corpus

Differential equations driven by Gaussian signals (2007, methodology): “We recall that such a support description in rough path topology yields, as consequence of Lyons’ limit theorem [17] and without further work, a Stroock-Varadhan type support theorem for solutions of rough path differential equations (RDEs) driven by the (random) geometric p-rough path X. For Browni”
A (rough) pathwise approach to a class of non-linear stochastic partial differential equations (2009, methodology): “In conjunction with known support properties of B (e.g. 33] in p -variation rough path topology or [16] for a conditional statement in Hölder rough path topology) continuity of the SPDE solution as a function of B immediately implies Stroock–Varadhan type support descriptions for such SPDEs.”
The Signature of a Rough Path: Uniqueness (2014, background): “Zhang [42], and to stochastic partial differential equations by M.”
A note on the notion of geometric rough paths (2004, methodology): “A support description was conjectured in [16] and we prove it here for H > 1/3.”
Densities for rough differential equations under Hormander's condition (2007, background): “[28] (who obtained it for the Brownian rough path) and carried out independently in [11, 15] for H > 1/3.”
Rough path analysis via fractional calculus (2006, methodology): “We refer, for instance, to [1], [3], [4] and [7] for recent applications of the rough path analysis to the stochastic calculus with respect to the Wiener process.”
Integrability Estimates for Gaussian Rough Differential Equations (2011, background): “Various recent works (Coutin and Qian [5], Ledoux, Qian and Zhang [23], Friz and Victoir [12], Lyons and Hambly [19]) have explored the use of rough paths to understand differential equations driven by nonsemimartingale noise processes.”
Malliavin Calculus for Fractional Delay Equations (2009, background): “This global program has already been started as far as moments estimates [13], large deviations [16], or properties of the law [2, 21] are concerned.”
Multidimensional Stochastic Processes as Rough Paths: Theory and Applications (2010, methodology): “Large deviations for EBM were first established in -variation rough path topology [94]; the 1-Hölder case was obtained in [58].”