Some SDEs with distributional drift.

By Franco Flandoli, Francesco Russo, J. Wolf. 2004

73 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/b488e384f865f7bc0fdb58de9a7985963c7fc749

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In Applied Mathematics

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Citations in the corpus

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], .”
Some parabolic PDEs whose drift is an irregular random noise in space (2006, background): “Even though in [10] we discuss the general case with related non-explosion conditions, here in order to ensure conservativeness we suppose that ∫ 0 −∞ e−Σ(x)dx = ∫ ∞”
Weak Dirichlet processes with a stochastic control perspective (2006, background): “The literature on Itô’s formula for nonsmooth functions of semimartingales or diffusion processes has known a lot of development in the recent years, see for instance [25] for non-degenerate Brownian martingales, [9] for non-degenerate 1-dimensional diffusions with bounded measurable drift or [7] in”
Multidimensional stochastic differential equations with distributional drift (2014, background): “The case of time independent SDEs in dimension one of the type (5) dXt = σ(Xt)dWt + b(Xt)dt, where σ is a strictly positive continuous function and b is the derivative of a real continuous function was solved and analyzed carefully in [7] and [8], which treated well-posedness of the martingale probl”
Elements of Stochastic Calculus via Regularization (2006, methodology): “Moreover if f ∈ W 1,2 loc , it is proved in [ 19 ] that (f (Xt)) is an (Ft)-Dirichlet process.”
A stochastic sewing lemma and applications (2018, background): “We will not ponder on this problem in the article, but rather refer readers to various examples in the literature, [14, 2, 25, 8, 5, 13].”