Geodesic
A note on weak solutions to stochastic differential equations
Kybernetika, Tome 54 (2018) no. 5, pp. 888-907
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We revisit the proof of existence of weak solutions of stochastic differential equations with continuous coeficients. In standard proofs, the coefficients are approximated by more regular ones and it is necessary to prove that: i) the laws of solutions of approximating equations form a tight set of measures on the paths space, ii) its cluster points are laws of solutions of the limit equation. We aim at showing that both steps may be done in a particularly simple and elementary manner.
We revisit the proof of existence of weak solutions of stochastic differential equations with continuous coeficients. In standard proofs, the coefficients are approximated by more regular ones and it is necessary to prove that: i) the laws of solutions of approximating equations form a tight set of measures on the paths space, ii) its cluster points are laws of solutions of the limit equation. We aim at showing that both steps may be done in a particularly simple and elementary manner.
DOI : 10.14736/kyb-2018-5-0888
Classification : 60H10
Keywords: stochastic differential equations; continuous coefficients; weak solutions 
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Ondreját, Martin; Seidler, Jan. A note on weak solutions to stochastic differential equations. Kybernetika, Tome 54 (2018) no. 5, pp. 888-907. doi: 10.14736/kyb-2018-5-0888

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