Let B be the 2-parameter
Brownian motion on D = [0,∞] × [0,∞) and Z be a 2-parameter stochastic process
defined on the boundary ∂D of D. Consider the non-Markovian stochastic differential
system in 2-parameter
Under the assumption that the coefficients α and β satisfy a Lipschitz condition and
a growth condition and the assumption that Z has continuous sample functions and
locally bounded second moment on ∂D, it is shown in this paper that the differential
system has a strong solution. Pathwise uniqueness of solution is established under the
assumption of the Lipschitz condition.
