Existence of strong solutions for Itô's stochastic equations via approximations

István Gyöngy; Nicolai Krylov

doi:10.1007/bf01203833

Existence of strong solutions for Itô's stochastic equations via approximations

István Gyöngy
, Nicolai Krylov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

311 Scopus citations

Abstract

Given strong uniqueness for an Itô's stochastic equation with discontinuous coefficients, we prove that its solution can be constructed on "any" probability space by using, for example, Euler's polygonal approximations. Stochastic equations in ℝ^d and in domains in ℝ^d are considered.

Original language	English (US)
Pages (from-to)	143-158
Number of pages	16
Journal	Probability Theory and Related Fields
Volume	105
Issue number	2
DOIs	https://doi.org/10.1007/bf01203833
State	Published - Jun 1996

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abstract = "Given strong uniqueness for an It{\^o}'s stochastic equation with discontinuous coefficients, we prove that its solution can be constructed on {"}any{"} probability space by using, for example, Euler's polygonal approximations. Stochastic equations in ℝd and in domains in ℝd are considered.",

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year = "1996",

month = jun,

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T1 - Existence of strong solutions for Itô's stochastic equations via approximations

AU - Gyöngy, István

AU - Krylov, Nicolai

PY - 1996/6

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N2 - Given strong uniqueness for an Itô's stochastic equation with discontinuous coefficients, we prove that its solution can be constructed on "any" probability space by using, for example, Euler's polygonal approximations. Stochastic equations in ℝd and in domains in ℝd are considered.

AB - Given strong uniqueness for an Itô's stochastic equation with discontinuous coefficients, we prove that its solution can be constructed on "any" probability space by using, for example, Euler's polygonal approximations. Stochastic equations in ℝd and in domains in ℝd are considered.

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U2 - 10.1007/bf01203833

DO - 10.1007/bf01203833

M3 - Article

AN - SCOPUS:0040361064

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VL - 105

SP - 143

EP - 158

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 2

ER -

Existence of strong solutions for Itô's stochastic equations via approximations

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