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

D. Nualart and J. Yeh

Stochastic Processes and their Applications, 1989, vol. 33, issue 1, 45-61

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.

Keywords: linear; stochastic; differential; equations; strong; solutions; continuous; dependence; on; the; boundary; conditions (search for similar items in EconPapers)
Date: 1989
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