# Infinite Interval Backward Stochastic Differential Equations in the Plane

Infinite Interval Backward Stochastic Differential Equations in the Plane This paper studies the existence and uniqueness of solution of infinite interval backward stochastic differential equation (BSDE) in the plane driven by a Brownian sheet. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Infinite Interval Backward Stochastic Differential Equations in the Plane

, Volume 19 (3) – Mar 3, 2017

## Infinite Interval Backward Stochastic Differential Equations in the Plane

Acta Mathematicae Applicatae Sinica, English Series Vol. 19, No. 3 (2003) 485–490 Inﬁnite Interval Backward Stochastic Diﬀerential Equations in the Plane Yan-ling Gu School of Mathematics and System Sciences, Shandong University, Jinan 250100, China (E-mail: guyl@math.sdu.edu.cn) Abstract This paper studies the existence and uniqueness of solution of inﬁnite interval backward stochastic diﬀerential equation (BSDE) in the plane driven by a Brownian sheet. Keywords Two-parameter mixed type BSDE 2000 MR Subject Classiﬁcation 60H10 1 Introduction Nonlinear backward stochastic diﬀerential equation (BSDE) has been independently introduced [4] [3] by Pardoux, Peng and by Duﬃe, Epstein . These authors proved the existence and unique- ness of an adapted pair of square integrable processes (Y ,Z ) satisfying t t t∈[0,T ] T T Y = ξ + f (s, Y ,Z )ds − Z dW,t ∈ [t, T ], t s s s s t t where W = {W ,t ∈ [0,T ]} is a standard d-dimensional Brownian motion deﬁned on a com- plete probability space (Ω ,F , P), and let {F } denote its nature ﬁltration, ξ is an F t 0≤t≤T T -measurable square integrable random variable and f (ω, t, y, z) is an adapted function which is [2] Lipschitz in (y, z). Later Chen, Wang extended this result to the inﬁnite time interval BSDE whose Lipschitz coeﬃcients can be unbounded and gave some applications. The theory provides a useful framework for formulating problems in mathematical ﬁnance and this motivates the work presented here. Backward stochastic diﬀerential equation in the plane driven by a two-parameter Brownian [8] motion is a new subject. Zaidi, Nualart ﬁrst studied this kind of equation, but in their paper there is a stringent condition imposed on the Lipschitzian constants. This paper purports to give a suﬃcient condition on the coeﬃcients of a class of inﬁnite interval BSDE, under which the inﬁnite interval BSDE has a unique solution for any given square...

/lp/springer_journal/infinite-interval-backward-stochastic-differential-equations-in-the-N0XsDV0xvh
Publisher
Springer Journals
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
D.O.I.
10.1007/s10255-003-0124-0
Publisher site
See Article on Publisher Site

### Abstract

This paper studies the existence and uniqueness of solution of infinite interval backward stochastic differential equation (BSDE) in the plane driven by a Brownian sheet.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 3, 2017

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