# Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized Burgers' equations

ESAIM: Probability and Statistics (2010)

- Volume: 1, page 339-355
- ISSN: 1292-8100

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topJourdain, Benjamin. "Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized Burgers' equations." ESAIM: Probability and Statistics 1 (2010): 339-355. <http://eudml.org/doc/197769>.

@article{Jourdain2010,

abstract = {
We prove existence and uniqueness for two classes of martingale problems
involving a nonlinear but bounded drift coefficient. In the first class,
this coefficient depends on the time t, the position x and the marginal
of the solution at time t. In the second, it depends on t, x and p(t,x),
the density of the time marginal w.r.t. Lebesgue measure. As far as the
dependence on t and x is concerned, no continuity assumption is made.
The results, first proved for the identity diffusion matrix, are extended
to bounded, uniformly elliptic and Lipschitz continuous matrices. As an
application, we show that within each class, a particular choice of the
coefficients leads to a probabilistic interpretation of generalizations
of Burgers' equation.
},

author = {Jourdain, Benjamin},

journal = {ESAIM: Probability and Statistics},

keywords = {Nonlinear martingale problem / Burgers equation /
interacting particle system / propagation of chaos.; martingale problems; identity diffusion matrix; Lipschitz continuous matrices; Burgers' equation},

language = {eng},

month = {3},

pages = {339-355},

publisher = {EDP Sciences},

title = {Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized Burgers' equations},

url = {http://eudml.org/doc/197769},

volume = {1},

year = {2010},

}

TY - JOUR

AU - Jourdain, Benjamin

TI - Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized Burgers' equations

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 1

SP - 339

EP - 355

AB -
We prove existence and uniqueness for two classes of martingale problems
involving a nonlinear but bounded drift coefficient. In the first class,
this coefficient depends on the time t, the position x and the marginal
of the solution at time t. In the second, it depends on t, x and p(t,x),
the density of the time marginal w.r.t. Lebesgue measure. As far as the
dependence on t and x is concerned, no continuity assumption is made.
The results, first proved for the identity diffusion matrix, are extended
to bounded, uniformly elliptic and Lipschitz continuous matrices. As an
application, we show that within each class, a particular choice of the
coefficients leads to a probabilistic interpretation of generalizations
of Burgers' equation.

LA - eng

KW - Nonlinear martingale problem / Burgers equation /
interacting particle system / propagation of chaos.; martingale problems; identity diffusion matrix; Lipschitz continuous matrices; Burgers' equation

UR - http://eudml.org/doc/197769

ER -

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