We find new conditions for existence of strong solutions of ordinary differential equations with random right-hand side, stochastic differential equations with measurable random drift, and their trajectory analogs with symmetric integrals. We show that solutions of Itô equations satisfy a parabolic equation along trajectories of a Wiener process.
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Nasyrov, F.S. On Strong Solutions of Stochastic Differential Equations and Their Trajectory Analogs. Sib. Adv. Math. 31, 147–153 (2021). https://doi.org/10.1134/S1055134421020048
- stochastic differential equation
- strong solution
- equation with symmetric integrals
- ordinary differential equation with random right-hand side
- Carathéodory solution
- Filippov solution