An example of a non-Markovian stochastic two-point boundary value problem
نویسنده
چکیده
with the af®ne boundary condition F0 X 0 F1 X 1 f : (1:2) Ocone and Pardoux (1989) provide necessary and suf®cient conditions for the existence and uniqueness of a solution and establish suf®cient conditions for the solution to be a Markov ®eld. The Markov ®eld property was studied by means of the co-area formula. In the Gaussian case (i.e., Bi 0 for all i) the Markov ®eld property is always true. In the nonGaussian case a suf®cient condition for the process fX tg to be a Markov ®eld is that a b1 . . . bk 0, and Ö tÖÿ1 s is a diagonal matrix for all 0 < s < t < 1, where Ö t is the d 3 d matrix-valued process solution of
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