Strong solutions of stochastic equations with singular time dependent drift

By Nicolai V. Krylov, Michael Röckner. 2005

540 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/a00c9fc61ba3a7b99c8b603f9b22f2f040cf0f98

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Sobolev differentiable stochastic flows for SDEs with singular coefficients: Applications to the transport equation (2012, background): “See, for example, [27] or [17] and the references therein.”
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]).”
Pathwise uniqueness and continuous dependence for SDEs with non-regular drift (2010, result): “gif"/> ifA remarkable result of Krylov and Rockner [ 7 ] states that this equation has a unique strong solution, in the class of continuous processes such thatThis result on strong solutions is the most advanced one in terms of generality of the drift; from this viewpoint it extends previous resul”
$L^q(L^p)$-theory of stochastic differential equations (2019, background): “When b ∈ Lq := ∩T>0Lq(T ) for some p, q ∈ [2,∞) with d p + 2 q < 1, by Girsanov’s transformation and some L p q -estimate for the associated Kolmogorov equation, Krylov and Röckner [9] showed the strong well-posedness for SDE (1.”
On the convergence of stochastic transport equations to a deterministic parabolic one (2019, background): “Observe that condition p1 > 2q1/(q1 − d) may be rewritten as 2 p1 + d q1 < 1 which is known in literature as Krylov-Rockner condition, see [19],[4].”
Noiseless regularisation by noise (2020, background): “Furthermore, a large set of theoretical tools is available to analyse the effect of Brownian perturbations to deterministic evolutions and this topic has a long and extensive literature [7, 13, 14, 21, 34, 51, 52].”
Stochastic flows of SDEs with irregular coefficients and stochastic transport equations (2009, background): “On the other hand, whenσ is non-degenerate andb is not continuous and even singular, SDE (1.1) may have a unique strong solution for each starting point x ∈ Rd (cf. [14, 17, 26], etc.).”
Selection of equilibria in a linear quadratic mean-field game (2018, background): “Several authors also contributed to the subject and addressed the higher dimensional framework, among which Veretennikov [49], Krylov and Röckner [31], Davie [15]... Similar questions have been also addressed in the framework of infinite dimensional stochastic differential equations, see for instan”
A stochastic sewing lemma and applications (2018, background): “When H = 1/2, a well-known result of Krylov and Röckner [30] states that (6.2) has unique strong solution if d p + 2 q < 1 ⇔ τ1/2(p, q) > 1 2 .”
Rough paths and 1d SDE with a time dependent distributional drift: application to polymers (2014, background): “When BxYt makes sense as a measurable function, with suitable integrability conditions, pathwise existence and uniqueness are known to hold: See the earlier papers by Zvonkin [32] and Veretennikov [30] when the derivative exists as a bounded function, in which case existence and uniqueness hold glob”