Degenerate SDEs in Hilbert spaces with rough drifts

Feng Yu Wang; Xicheng Zhang

doi:10.1142/S0219025715500265

Degenerate SDEs in Hilbert spaces with rough drifts

Feng Yu Wang
, Xicheng Zhang

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

14 Citations (Scopus)

Abstract

The existence and uniqueness of mild solutions are proved for a class of degenerate stochastic differential equations on Hilbert spaces where the drift is Dini continuous in the component with noise and Hölder continuous of order larger than 2/3 in the other component. In the finite-dimensional case the Dini continuity is further weakened. The main results are applied to solve second order stochastic systems driven by spacetime white noises.

Original language	English
Article number	1550026
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	18
Issue number	4
DOIs	https://doi.org/10.1142/S0219025715500265
Publication status	Published - 1 Dec 2015
Externally published	Yes

Keywords

Degenerate evolution equation
mild solution
regularization transform

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10.1142/S0219025715500265

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title = "Degenerate SDEs in Hilbert spaces with rough drifts",

abstract = "The existence and uniqueness of mild solutions are proved for a class of degenerate stochastic differential equations on Hilbert spaces where the drift is Dini continuous in the component with noise and H{\"o}lder continuous of order larger than 2/3 in the other component. In the finite-dimensional case the Dini continuity is further weakened. The main results are applied to solve second order stochastic systems driven by spacetime white noises.",

keywords = "Degenerate evolution equation, mild solution, regularization transform",

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AU - Wang, Feng Yu

AU - Zhang, Xicheng

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N2 - The existence and uniqueness of mild solutions are proved for a class of degenerate stochastic differential equations on Hilbert spaces where the drift is Dini continuous in the component with noise and Hölder continuous of order larger than 2/3 in the other component. In the finite-dimensional case the Dini continuity is further weakened. The main results are applied to solve second order stochastic systems driven by spacetime white noises.

AB - The existence and uniqueness of mild solutions are proved for a class of degenerate stochastic differential equations on Hilbert spaces where the drift is Dini continuous in the component with noise and Hölder continuous of order larger than 2/3 in the other component. In the finite-dimensional case the Dini continuity is further weakened. The main results are applied to solve second order stochastic systems driven by spacetime white noises.

KW - Degenerate evolution equation

KW - mild solution

KW - regularization transform

UR - https://www.scopus.com/pages/publications/84954397467

U2 - 10.1142/S0219025715500265

DO - 10.1142/S0219025715500265

M3 - Article

AN - SCOPUS:84954397467

SN - 0219-0257

VL - 18

JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics

JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

IS - 4

M1 - 1550026

ER -

Degenerate SDEs in Hilbert spaces with rough drifts

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Keywords

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