QUADRATIC FBSDE WITH GENERALIZED BURGERS' TYPE NONLINEARITIES, PERTURBATIONS AND LARGE DEVIATIONS

Christoph Frei; Goncalo Dos Reis

doi:10.1142/S0219493712500153

QUADRATIC FBSDE WITH GENERALIZED BURGERS' TYPE NONLINEARITIES, PERTURBATIONS AND LARGE DEVIATIONS

Christoph Frei, Goncalo Dos Reis^*

^*Corresponding author for this work

School of Mathematics

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

Abstract

We discuss BSDE with drivers containing nonlinearities of the type p(y)vertical bar z vertical bar and p(y)vertical bar z vertical bar(2) with p a polynomial of any degree. Sufficient conditions are given for the existence and uniqueness of solutions as well as comparison results. We then connect the results to the Markovian FBSDE setting, discussing applications in the theory of PDE perturbation and stating a result concerning a large deviations principle for the first component of the solution to the BSDE.

Original language	English
Article number	1250015
Number of pages	37
Journal	Stochastics and dynamics
Volume	13
Issue number	2
DOIs	https://doi.org/10.1142/S0219493712500153
Publication status	Published - Jun 2013

Keywords

FBSDE
quadratic growth BSDE
generalized Burgers' PDE
PDE perturbation
large deviations principle
Navier-Stokes
STOCHASTIC DIFFERENTIAL-EQUATIONS
HARMONIC MAPS
HEAT-FLOW
GROWTH
BSDES
CONVERGENCE
PDES
TIME

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10.1142/S0219493712500153

QUADRATIC FBSDE WITH GENERALIZED BURGERS' TYPE NONLINEARITIES, PERTURBATIONS AND LARGE DEVIATIONS
Electronic version of an article published as [Stochastics and Dynamics, Volume 13, Issue 02, June 2013, 37 Pages] [Article DOI 10.1142/S0219493712500153] © [copyright World Scientific Publishing Company] [http://www.worldscientific.com/doi/abs/10.1142/S0219493712500153?queryID=31%2F574902]
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title = "QUADRATIC FBSDE WITH GENERALIZED BURGERS' TYPE NONLINEARITIES, PERTURBATIONS AND LARGE DEVIATIONS",

abstract = "We discuss BSDE with drivers containing nonlinearities of the type p(y)vertical bar z vertical bar and p(y)vertical bar z vertical bar(2) with p a polynomial of any degree. Sufficient conditions are given for the existence and uniqueness of solutions as well as comparison results. We then connect the results to the Markovian FBSDE setting, discussing applications in the theory of PDE perturbation and stating a result concerning a large deviations principle for the first component of the solution to the BSDE.",

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author = "Christoph Frei and {Dos Reis}, Goncalo",

year = "2013",

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doi = "10.1142/S0219493712500153",

language = "English",

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AU - Dos Reis, Goncalo

PY - 2013/6

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AB - We discuss BSDE with drivers containing nonlinearities of the type p(y)vertical bar z vertical bar and p(y)vertical bar z vertical bar(2) with p a polynomial of any degree. Sufficient conditions are given for the existence and uniqueness of solutions as well as comparison results. We then connect the results to the Markovian FBSDE setting, discussing applications in the theory of PDE perturbation and stating a result concerning a large deviations principle for the first component of the solution to the BSDE.

KW - FBSDE

KW - quadratic growth BSDE

KW - generalized Burgers' PDE

KW - PDE perturbation

KW - large deviations principle

KW - Navier-Stokes

KW - STOCHASTIC DIFFERENTIAL-EQUATIONS

KW - HARMONIC MAPS

KW - HEAT-FLOW

KW - GROWTH

KW - BSDES

KW - CONVERGENCE

KW - PDES

KW - TIME

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DO - 10.1142/S0219493712500153

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VL - 13

JO - Stochastics and dynamics

JF - Stochastics and dynamics

SN - 0219-4937

IS - 2

M1 - 1250015

ER -

QUADRATIC FBSDE WITH GENERALIZED BURGERS' TYPE NONLINEARITIES, PERTURBATIONS AND LARGE DEVIATIONS

Abstract

Keywords

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