Well-posedness of backward stochastic partial differential equations with Lyapunov condition

  • 1 Department of Mathematics, Beijing Institute of Technology, 100081, Beijing, P. R. China
  • 2 School of Mathematics and Statistics, Jiangsu Normal University, 221116, Xuzhou, P. R. China
Wei Liu and Rongchan Zhu
  • Corresponding author
  • Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, P. R. China, and Department of Mathematics, University of Bielefeld, 33615 Bielefeld, Germany
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Abstract

In this paper we show the existence and uniqueness of strong solutions for a large class of backward SPDEs, where the coefficients satisfy a specific type Lyapunov condition instead of the classical coercivity condition. Moreover, based on the generalized variational framework, we also use the local monotonicity condition to replace the standard monotonicity condition, which is applicable to various quasilinear and semilinear BSPDE models.

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