Construction of strong solutions of SDE's via Malliavin calculus

By T. Meyer‐Brandis, Frank Norbert Proske. 2010

75 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/293f80d7c6d0b7ba96766f74de005b7255f3990d

How researchers see this paper

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

In Economics and Econometrics

1. Franco Flandoli
2. E. Fedrizzi
3. Torstein Nilssen
4. Frank Norbert Proske
5. Salah-Eldin A. Mohammed
6. Martin Bauer
7. R. Lassalle
8. T. Meyer‐Brandis

In Finance

1. Xicheng Zhang
2. Franco Flandoli
3. Massimiliano Gubinelli
4. E. Fedrizzi
5. Frank Norbert Proske
6. Torstein Nilssen
7. Salah-Eldin A. Mohammed
8. Rémi Catellier

In Management Science and Operations Research

1. E. Fedrizzi
2. Franco Flandoli
3. T. Meyer‐Brandis
4. Frank Norbert Proske
5. Martin Bauer
6. Torstein Nilssen
7. R. Lassalle
8. Tusheng Zhang

Citations in the corpus

• Averaging along irregular curves and regularisation of ODEs (2012, background): “and Priola [8], Zhang, Flandoli and Da Prato [6]. All these work are essentially based of the use of Itˆo calculus to highlight the regularising properties of Brownian paths. Meyer-Brandis and Proske [17] use Malliavin calculus to derive similar conclusions. Davie’s contribution [7] is more subtle i”
• A variational approach to the construction and Malliavin differentiability of strong solutions of SDE’s (2013, methodology): “Let us also mention that we considerably improve the 200 technique initiated in [28] (see also [26] and [34]) by removing a certain symmetry condition on 201 the drift coefficients in (3.”
• Sobolev differentiable stochastic flows for SDEs with singular coefficients: Applications to the transport equation (2012, background): “An alternative approach, which does not rely on a pathwise uniqueness argument and which also yields the Malliavin differentiability of solutions to (1) was recently developed in [27] and [26].”
• Noise Prevents Singularities in Linear Transport Equations (2012, methodology): “te increments has been given in [13]. Here we establish Sobolev type differentiability. A similar Sobolev regularity of the flow is investigated in [20] by different tools (Malliavin calculus). See also [19]. The assumption (1) has been introduced in the framework of stochastic differential equations by”
• Strong Solutions of Mean-Field Stochastic Differential Equations with irregular drift (2018, methodology): “This re-interpretation allows to apply the ideas and techniques developed in [2],[31] and [33] on strong solutions of SDEs with irregular coefficients to equation (6).”
• Causal transport plans and their Monge–Kantorovich problems (2013, background): “1) encompass the Markovian diffusions investigated by Zvonkin (see [19], [52], [46] and also [27] for a recent contribution) as well as the famous Cirelson’s equation (see[18]).”