## Bernoulli

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

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

#### 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**

Received: March 2015

Revised: January 2016

First available in Project Euclid: 21 September 2017

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.3150/16-BEJ816

**Mathematical Reviews number (MathSciNet)**

MR3706782

**Zentralblatt MATH identifier**

06778353

**Keywords**

backward stochastic partial differential equation Hörmander theorem Itô process non-Markov

#### 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