Nonlinear backward stochastic evolutionary equations driven by a space-time white noise

Ying Hu; Shanjian Tang

doi:10.3934/mcrf.2018032

Article Contents

2018, Volume 8, Issue 3&4: 739-751. Doi: 10.3934/mcrf.2018032

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Nonlinear backward stochastic evolutionary equations driven by a space-time white noise

Ying Hu^1,2, and
Shanjian Tang^3, ,

1.
Institut de Recherche Mathématique de Rennes, Université Rennes 1, 35042 Rennes Cedex, France
2.
School of Mathematical Sciences, Fudan University, Shanghai 200433, China
3.
Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, Shanghai 200433, China

* Corresponding authorr: Shanjian Tang
* Corresponding authorr: Shanjian Tang

Received: August 2017

Revised: April 2018

Published: September 2018

Ying Hu's research is partially supported by Lebesgue Center of Mathematics "Investissements d'avenir" Program (No. ANR-11-LABX-0020-01), by ANR CAESARS (No. ANR-15-CE05-0024) and by ANR MFG (No. ANR-16-CE40-0015-01). Shanjian Tang's research is partially supported by National Science Foundation of China (No. 11631004) and Science and Technology Commission of Shanghai Municipality (No. 14XD1400400)

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Abstract

We study the well solvability of nonlinear backward stochastic evolutionary equations driven by a space-time white noise. We first establish a novel a priori estimate for solution of linear backward stochastic evolutionary equations, and then give an existence and uniqueness result for nonlinear backward stochastic evolutionary equations. A dual argument plays a crucial role in the proof of these results. Finally, an example is given to illustrate the existence and uniqueness result.

Keywords:

Backward stochastic evolutionary equation,
space-time white noise,
well solvability,
a priori estimate,
dual argument.

Mathematics Subject Classification: Primary: 60H15, 35R60.

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