# American Institute of Mathematical Sciences

January  2019, 4: 3 doi: 10.1186/s41546-019-0037-3

## The Cauchy problem of Backward Stochastic Super-Parabolic Equations with Quadratic Growth

 1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China; 2. Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, and Key Laboratory of Mathematics for Nonlinear Sciences(Fudan University), Ministry of Education, Shanghai 200433, China

Received  November 26, 2018 Revised  March 12, 2019

Fund Project: Both Qiu and Tang acknowledge research supported by the National Science Foundation of China (Grants Nos. 11631004 and 11171076), by the Science and Technology Commission, Shanghai Municipality (Grant No. 14XD1400400), and by the Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University.

The paper is devoted to the Cauchy problem of backward stochastic superparabolic equations with quadratic growth. We prove two Itô formulas in the whole space. Furthermore, we prove the existence of weak solutions for the case of one-dimensional state space, and the uniqueness of weak solutions without constraint on the state space.
Citation: Renzhi Qiu, Shanjian Tang. The Cauchy problem of Backward Stochastic Super-Parabolic Equations with Quadratic Growth. Probability, Uncertainty and Quantitative Risk, 2019, 4 (0) : 3-. doi: 10.1186/s41546-019-0037-3
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