Kybernetika 54 no. 5, 888-907, 2018

A note on weak solutions to stochastic differential equations

Martin Ondreját and Jan SeidlerDOI: 10.14736/kyb-2018-5-0888

Abstract:

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.

Keywords:

stochastic differential equations, continuous coefficients, weak solutions

Classification:

60H10

paper.pdf

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