Some SDEs with distributional drift. Part II: Lyons-Zheng structure, Itô's formula and semimartingale characterization

Franco Flandoli; Francesco Russo; Jochen Wolf

doi:10.1163/156939704323074700

Some SDEs with distributional drift. Part II: Lyons-Zheng structure, Itô's formula and semimartingale characterization

Franco Flandoli
, Francesco Russo
, Jochen Wolf

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

Abstract

In dimension 1 we study a martingale problem related to a parabolic PDE operator L with continuous (non-degenerate) diffusion term and with drift being the derivative of a continuous function. We state a necessary and sufficient condition on f and the solution X such that f(X) is a semimartingale. When X is a semimartingale, we also establish an Itô formula for f(X) under minimal assumptions. Particular attention is devoted to the case when L is close to divergence form.

Original language	English
Pages (from-to)	145-184
Number of pages	40
Journal	Random Operators and Stochastic Equations
Volume	12
Issue number	2
DOIs	https://doi.org/10.1163/156939704323074700
Publication status	Published - 1 Dec 2004
Externally published	Yes

Keywords

Distributional drift
Lyons-Zheng processes
Martingale problems
Time reversal

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10.1163/156939704323074700

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title = "Some SDEs with distributional drift. Part II: Lyons-Zheng structure, It{\^o}'s formula and semimartingale characterization",

abstract = "In dimension 1 we study a martingale problem related to a parabolic PDE operator L with continuous (non-degenerate) diffusion term and with drift being the derivative of a continuous function. We state a necessary and sufficient condition on f and the solution X such that f(X) is a semimartingale. When X is a semimartingale, we also establish an It{\^o} formula for f(X) under minimal assumptions. Particular attention is devoted to the case when L is close to divergence form.",

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author = "Franco Flandoli and Francesco Russo and Jochen Wolf",

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T2 - Lyons-Zheng structure, Itô's formula and semimartingale characterization

AU - Flandoli, Franco

AU - Russo, Francesco

AU - Wolf, Jochen

PY - 2004/12/1

Y1 - 2004/12/1

N2 - In dimension 1 we study a martingale problem related to a parabolic PDE operator L with continuous (non-degenerate) diffusion term and with drift being the derivative of a continuous function. We state a necessary and sufficient condition on f and the solution X such that f(X) is a semimartingale. When X is a semimartingale, we also establish an Itô formula for f(X) under minimal assumptions. Particular attention is devoted to the case when L is close to divergence form.

AB - In dimension 1 we study a martingale problem related to a parabolic PDE operator L with continuous (non-degenerate) diffusion term and with drift being the derivative of a continuous function. We state a necessary and sufficient condition on f and the solution X such that f(X) is a semimartingale. When X is a semimartingale, we also establish an Itô formula for f(X) under minimal assumptions. Particular attention is devoted to the case when L is close to divergence form.

KW - Distributional drift

KW - Lyons-Zheng processes

KW - Martingale problems

KW - Time reversal

U2 - 10.1163/156939704323074700

DO - 10.1163/156939704323074700

M3 - Article

AN - SCOPUS:33749235993

SN - 0926-6364

VL - 12

SP - 145

EP - 184

JO - Random Operators and Stochastic Equations

JF - Random Operators and Stochastic Equations

IS - 2

ER -

Some SDEs with distributional drift. Part II: Lyons-Zheng structure, Itô's formula and semimartingale characterization

Abstract

Keywords

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