Construction of strong solutions of SDE's via Malliavin calculus

@article{MeyerBrandis2010ConstructionOS,
  title={Construction of strong solutions of SDE's via Malliavin calculus},
  author={Thilo Meyer-Brandis and Frank Proske},
  journal={Journal of Functional Analysis},
  year={2010},
  volume={258},
  pages={3922-3953}
}
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61 Citations
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61 Citations

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References

SHOWING 1-10 OF 35 REFERENCES
Stochastic differential equations—some new ideas
In this paper we present a general method to study stochastic equations for a broader class of driving noises. We explain the main principles of this approach in the case of stochastic differential…
Strong solutions of stochastic equations with singular time dependent drift
Abstract.We prove existence and uniqueness of strong solutions to stochastic equations in domains with unit diffusion and singular time dependent drift b up to an explosion time. We only assume local…
A class of stochastic differential equations with non-Lipschitzian coefficients: pathwise uniqueness and no explosion
On the existence and explicit representability of strong solutions of Lévy noise driven SDE's with irregular coefficients
We give a method to represent strong solutions of stochastic differential equations driven by Levy processes, explicitly. Furthermore we employ these explicit representations to study strong…
Existence of strong solutions for Itô's stochastic equations via approximations
SummaryGiven strong uniqueness for an Itô's stochastic equation with discontinuous coefficients, we prove that its solution can be constructed on “any” probability space by using, for example,…
Malliavin calculus for Levy processes with applications to finance
Extending Gaussian Malliavin derivatives, to a finite moments Levy process framework, using chaos expansions has proven to be a successful approach. In this work the theory is extended by the…
Explicit Representation of Strong Solutions of SDEs Driven by Infinite-Dimensional Lévy Processes
We develop a white noise framework for Lévy processes on Hilbert spaces. As the main result of this paper, we then employ these white noise techniques to explicitly represent strong solutions of…
Malliavin Calculus for Lévy Processes with Applications to Finance
The Continuous Case: Brownian Motion.- The Wiener-Ito Chaos Expansion.- The Skorohod Integral.- Malliavin Derivative via Chaos Expansion.- Integral Representations and the Clark-Ocone formula.- White…
ON EXPLICIT STRONG SOLUTION OF ITÔ–SDE'S AND THE DONSKER DELTA FUNCTION OF A DIFFUSION
We determine a new explicit representation of strong solutions of Ito-diffusions and elicit its correspondence to the general stochastic transport equation. We apply this formula to deduce an…
Dirichlet Forms and Analysis on Wiener Space
The subject of this book is analysis on Wiener space by means of Dirichlet forms and Malliavin calculus. There are already several literature on this topic, but this book has some different…
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