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pr.chance – Conditions for actuality of a semi-martingale representing a system of chance measures Answer

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pr.chance – Conditions for actuality of a semi-martingale representing a system of chance measures

Let $(nu_t)_{t in [0,1]}$ breathe Borel chance measures on a stochastic foundation $(Omega,mathcal{F},(mathcal{F}_{t in [0,1]})_t,mathbb{P})$.

Does there live a semi-martingale $(X_t)_{tin[0,1]}$ on this stochastic foundation, such that $X_tsim nu_t$ for everty $t in [0,1]$? If not, what circumstances are wanted on the measures $nu_{cdot}$ for this to breathe workable?

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