Path-by-path uniqueness of multidimensional SDE’s on the plane with nondecreasing coefficients

نویسندگان

چکیده

In this paper we study path-by-path uniqueness for multidimensional stochastic differential equations driven by the Brownian sheet. We assume that drift coefficient is unbounded, verifies a spatial linear growth condition and componentwise nondeacreasing. Our approach consists of showing result bounded nondecreasing using both local time-space representation law iterated logarithm sheets. The desired follows Gronwall type lemma on plane. As product, obtain existence unique strong solution SDEs sheet when non-decreasing satisfies condition.

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ژورنال

عنوان ژورنال: Electronic Journal of Probability

سال: 2022

ISSN: ['1083-6489']

DOI: https://doi.org/10.1214/22-ejp844