Bernoulli

  • Bernoulli
  • Volume 19, Number 1 (2013), 93-114.

A numerical scheme for backward doubly stochastic differential equations

Auguste Aman

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Abstract

In this paper we propose a numerical scheme for the class of backward doubly stochastic differential equations (BDSDEs) with possible path-dependent terminal values. We prove that our scheme converges in the strong $L^{2}$-sense and derives its rate of convergence. As an intermediate step we derive an $L^{2}$-type regularity of the solution to such BDSDEs. Such a notion of regularity, which can be thought of as the modulus of continuity of the paths in an $L^{2}$-sense, is new.

Article information

Source
Bernoulli, Volume 19, Number 1 (2013), 93-114.

Dates
First available in Project Euclid: 18 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1358531742

Digital Object Identifier
doi:10.3150/11-BEJ391

Mathematical Reviews number (MathSciNet)
MR3019487

Zentralblatt MATH identifier
1274.60217

Keywords
backward doubly SDEs $L^{\infty}$-Lipschitz functionals $L^{2}$-regularity numerical scheme regression estimation

Citation

Aman, Auguste. A numerical scheme for backward doubly stochastic differential equations. Bernoulli 19 (2013), no. 1, 93--114. doi:10.3150/11-BEJ391. https://projecteuclid.org/euclid.bj/1358531742


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