## Bernoulli

• Bernoulli
• Volume 24, Number 2 (2018), 956-970.

### Hörmander-type theorem for Itô processes and related backward SPDEs

Jinniao Qiu

#### Abstract

A Hörmander-type theorem is established for Itô processes and related backward stochastic partial differential equations (BSPDEs). A short self-contained proof is also provided for the $L^{2}$-theory of linear, possibly degenerate BSPDEs, in which new gradient estimates are obtained.

#### Article information

Source
Bernoulli, Volume 24, Number 2 (2018), 956-970.

Dates
Revised: January 2016
First available in Project Euclid: 21 September 2017

https://projecteuclid.org/euclid.bj/1505980884

Digital Object Identifier
doi:10.3150/16-BEJ816

Mathematical Reviews number (MathSciNet)
MR3706782

Zentralblatt MATH identifier
06778353

#### Citation

Qiu, Jinniao. Hörmander-type theorem for Itô processes and related backward SPDEs. Bernoulli 24 (2018), no. 2, 956--970. doi:10.3150/16-BEJ816. https://projecteuclid.org/euclid.bj/1505980884

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