Summary
Let ξ(t) be a stochastic process starting from 0 with Ito differential
where\(\left( {W\left( t \right),\mathfrak{F}_t } \right)\) is a Wiener process, δ and β are bounded\(\mathfrak{F}\) processes such that δδT is uniformly positive definite. Then it is proved that there exists a stochastic differential equation
with non-random coefficients which admits a weak solutionx(t) having the same one-dimensional probability distribution as ξ(t) for everyt. The coefficients σ andb have a simple interpretation:
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This paper was written while the author was visiting the J.W. Goethe-University in Frankfurt as a fellow of the Alexander v. Humboldt Foundation
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Gyöngy, I. Mimicking the one-dimensional marginal distributions of processes having an ito differential. Probab. Th. Rel. Fields 71, 501–516 (1986). https://doi.org/10.1007/BF00699039
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DOI: https://doi.org/10.1007/BF00699039