Regularity of Wiener functionals under a Hörmander type condition of order one

Bally, Vlad; Caramellino, Lucia

doi:10.1214/16-aop1092

Cited by 1 publication

(2 citation statements)

References 12 publications

(25 reference statements)

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“…Sometimes it is easy to construct such a family with explicit densities p F δ and then one may check (2.27) directly (this is the case in the examples in Section 3.1 and 3.2). But sometimes one does not know p F δ and then it is useful to use the integration by parts machinery in order to prove (2.27) -this is the case in the example given is Section 3.3 or the application to a kind of generalization of the Hörmander condition to general Wiener functionals developed in [4].…”

Section: Random Variables and Integration By Partsmentioning

confidence: 99%

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Convergence and regularity of probability laws by using an interpolation method

Bally¹,

Caramellino²

2017

Ann. Probab.

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In [18] Fournier and Printems establish a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with Hölder continuous coefficients. This is of course out of reach by using already classical probabilistic methods based on Malliavin calculus. In [11] Debussche and Romito employ some Besov space technics in order to substantially improve the result of Fournier and Printems. In our paper we show that this kind of problem naturally fits in the framework of interpolation spaces: we prove an interpolation inequality (see Proposition 2.5) which allows to state (and even to slightly improve) the above absolute continuity result. Moreover it turns out that the above interpolation inequality has applications in a completely different framework: we use it in order to estimate the error in total variance distance in some convergence theorems.

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Section: Random Variables and Integration By Partsmentioning

confidence: 99%

“…Following the ideas in [27] we consider a function a : 4] and such that a(t) + a(4t) = 1 for t ∈ [ 1 4 , 1]. We may construct a in the following way: we take a function a : [0, 1] → R + with a(t) = 0 for t ≤ 1 4 and a(1) = 1.…”

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confidence: 99%