Existence of strong solutions for It\^o’s stochastic equations via approximations. Revisited

Istvan Gyongy, N.V. Krylov

Research output: Contribution to journalArticlepeer-review

Abstract

Given strong uniqueness for an Itô's stochastic equation, we prove that its solution can beconstructed on "any" probability space by using, for example, Euler's polygonal approximations. Stochastic equations in Rd and in domains in Rd are considered. This is almost a copy of an old article in which we correct errors in the original proof of Lemma 4.1 found by Martin Dieckmann in 2013. We present also a new result on the convergence of "tamed Euler approximations" for SDEs with locally unbounded drifts, which we achieve by proving an estimate for appropriate exponential moments.
Original languageEnglish
Number of pages24
JournalStochastics and Partial Differential Equations: Analysis and Computations
Publication statusAccepted/In press - 15 Oct 2021

Fingerprint

Dive into the research topics of 'Existence of strong solutions for It\^o’s stochastic equations via approximations. Revisited'. Together they form a unique fingerprint.

Cite this