Vol. 52, No. 1, 1974

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Existence and adjoint theorems for linear stochastic differential equations

V. M. Warfield

Vol. 52 (1974), No. 1, 305–320

This paper contains three theorems on linear stochastic differential equations, where the differential equations are given in terms of McShane’s first and second order related integrals. The first, which is modelled on the classical Picard Theorem, concerns the existence of solutions, the second gives boundedness of their moments, and the third provides them with adjoints. The Adjoint Theorem has the interesting property that its formulation requires the second order integral even when the original differential equation involves only the more standard first order integral.

Mathematical Subject Classification 2000
Primary: 60H10
Received: 1 November 1973
Published: 1 May 1974
V. M. Warfield