Brownian motion with singular drift

By Richard F. Bass, Zhen-Qing Chen. 2003

105 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c7bcc375d3bf6285ae3da6632bb71a0fdcb553c0

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Citations in the corpus

Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness (2014, background): “There are some results on weak well-posedness for measure-valued drifts, see [9], and distribution-valued drifts, see [44, 28, 15], but it is unclear whether they apply to the limit case p = d: for example, the result in [9], when restricted to measures with density b with respect to the Lebesgue me”
Parametrix construction of the transition probability density of the solution to an SDE driven by $\alpha$-stable noise (2014, background): “The technique therein is closely related to those introduced (in the diffusive setting) in [4], and apparently strongly relies on the structural assumption that the resolvent, which corresponds to pt (x, y), is a perturbation of the resolvent of an α-stable process.”
Stable process with singular drift (2014, background): “Here is the definition of an α-stable process with drift on R d , which is motivated by the definition of a Brownian motion with singular drift introduced in [4].”
Uniqueness of stable processes with drift (2013, methodology): “However, the existence and uniqueness of the solution in [7] is formulated in a weaker sense, as in [2].”
On the constructions of the skew Brownian motion (2007, background): “As the local time plays a central role in the theory of one-dimensional diffusion processes, SDE with local times are also considered in the study of diffusions with singular drift, in order to get some diffusions under weak hypotheses (see for example [9, 10, 30], .”
Two-sided estimates on the density of Brownian motion with singular drift (2006, unknown): “The following definition is taken from [4] d ) is such that each µ i is a signed measure on R d belonging to the Kato class K d,1 .”
A stochastic sewing lemma and applications (2018, methodology): “Condition (iii) is inspired by the work [2] of Bass and Chen.”