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Dependence on the boundary condition for linear stochastic differential equations in the plane

Author

Listed:
  • Nualart, D.
  • Yeh, J.

Abstract

An expression for the strong solution of the linear stochastic differential equation in the plane is obtained giving the solution as a function of the boundary condition. It is shown that the boundary condition as a function defined on the boundary of 2+ is transformed continuously by the solution of the stochastic differential equation as the two dimensional "time" progresses. Also the continuity of the solution jointly in 2+ and the space of boundary conditions is established.

Suggested Citation

  • Nualart, D. & Yeh, J., 1989. "Dependence on the boundary condition for linear stochastic differential equations in the plane," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 45-61, October.
    • Handle: RePEc:eee:spapps:v:33:y:1989:i:1:p:45-61
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