# American Institute of Mathematical Sciences

September  2018, 8(3&4): 739-751. doi: 10.3934/mcrf.2018032

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

 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

Received  August 2017 Revised  April 2018 Published  September 2018

Fund Project: 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)

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.

Citation: Ying Hu, Shanjian Tang. Nonlinear backward stochastic evolutionary equations driven by a space-time white noise. Mathematical Control & Related Fields, 2018, 8 (3&4) : 739-751. doi: 10.3934/mcrf.2018032
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