Pathwise uniqueness for a class of SDE in Hilbert spaces and applications

By Giuseppe Da Prato, Franco Flandoli. 2010

86 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cb86914c6028edc3569ffe46173580eda4c5f374

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Citations in the corpus

Pathwise uniqueness for singular SDEs driven by stable processes (2010, background): “ able to prove uniqueness when b: Rd→ Rdis only Borel and bounded and Lis a standard d-dimensional Wiener process. This result has been generalized in various directions in [9], [13], [25], [6], [7], [5], [8]. The situation changes when Lis not a Wiener process but is a symmetric α-stable process, α”
Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift (2014, methodology): “Comparing with the above mentioned results of [5, 6, 7], Theorem 1.”
Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift (2011, methodology): “rov equations. Such regularity results, leading to continuity or smoothness of the solutions, however, do not hold in inﬁnite dimensions. A technique diﬀerent from [Ve80] is used in [FGP10] (see also [DF10], [FF10] and [Pr10]). This technique allows to prove uniqueness for stochastic equations with ”
Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients (2014, methodology): “ere an interesting open question is that whether we can extend the above characterization to the inﬁnite dimensional case in somehow so tha t it can be used to the SDE in Hilbert spaces as studied in [7, 8, 9, 10]. Now, we turn to the study of SDE (1.1) and make the following assumptions on σ and b.”
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].”
Averaging along irregular curves and regularisation of ODEs (2012, background): “ations (SDEs) driven by Brownian motion is nowadays a well understood subject: see for example Veretennikov, Krylov and Roeckner [15], Flandoli, Gubinelli 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 ”