# Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications

ESAIM: Probability and Statistics (2010)

- Volume: 9, page 74-97
- ISSN: 1292-8100

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topGautier, Éric. "Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications." ESAIM: Probability and Statistics 9 (2010): 74-97. <http://eudml.org/doc/104342>.

@article{Gautier2010,

abstract = {
Sample path large deviations
for the laws of the solutions of stochastic nonlinear
Schrödinger equations when the noise converges to zero are
presented. The noise is a complex additive Gaussian noise. It is
white in time and colored in space. The solutions may be global or
blow-up in finite time, the two cases are distinguished. The
results are stated in trajectory spaces endowed with topologies
analogue to projective limit topologies. In this setting, the
support of the law of the solution is also characterized. As a
consequence, results on the law of the blow-up time and
asymptotics when the noise converges to zero are obtained. An
application to the transmission of solitary waves in fiber optics
is also given.
},

author = {Gautier, Éric},

journal = {ESAIM: Probability and Statistics},

keywords = {Large deviations;
stochastic partial differential equations; nonlinear
Schrödinger equations;
white noise; projective limit; support theorem;
blow-up; solitary waves.; stochastic partial differential equations; nonlinear Schrödinger equations; white noise; blow-up; solitary waves},

language = {eng},

month = {3},

pages = {74-97},

publisher = {EDP Sciences},

title = {Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications},

url = {http://eudml.org/doc/104342},

volume = {9},

year = {2010},

}

TY - JOUR

AU - Gautier, Éric

TI - Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 9

SP - 74

EP - 97

AB -
Sample path large deviations
for the laws of the solutions of stochastic nonlinear
Schrödinger equations when the noise converges to zero are
presented. The noise is a complex additive Gaussian noise. It is
white in time and colored in space. The solutions may be global or
blow-up in finite time, the two cases are distinguished. The
results are stated in trajectory spaces endowed with topologies
analogue to projective limit topologies. In this setting, the
support of the law of the solution is also characterized. As a
consequence, results on the law of the blow-up time and
asymptotics when the noise converges to zero are obtained. An
application to the transmission of solitary waves in fiber optics
is also given.

LA - eng

KW - Large deviations;
stochastic partial differential equations; nonlinear
Schrödinger equations;
white noise; projective limit; support theorem;
blow-up; solitary waves.; stochastic partial differential equations; nonlinear Schrödinger equations; white noise; blow-up; solitary waves

UR - http://eudml.org/doc/104342

ER -

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