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Backward stochastic differential equations driven by [formula omitted]-Brownian motion

Authors
Journal
Stochastic Processes and their Applications
0304-4149
Publisher
Elsevier
Volume
124
Issue
1
Identifiers
DOI: 10.1016/j.spa.2013.09.010
Keywords
  • [Formula Omitted]-Expectation
  • [Formula Omitted]-Brownian Motion
  • [Formula Omitted]-Martingale
  • Backward Sdes
Disciplines
  • Mathematics

Abstract

Abstract In this paper, we study the backward stochastic differential equations driven by a G-Brownian motion (Bt)t≥0 in the following form: Yt=ξ+∫tTf(s,Ys,Zs)ds+∫tTg(s,Ys,Zs)d〈B〉s−∫tTZsdBs−(KT−Kt), where K is a decreasing G-martingale. Under Lipschitz conditions of f and g in Y and Z, the existence and uniqueness of the solution (Y,Z,K) of the above BSDE in the G-framework is proved.

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