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On Strong Solutions of Stochastic Differential Equations and Their Trajectory Analogs


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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The author is grateful to Professor Albert N. Shiryaev who drew author’s attention to problems connected with strong solutions of stochastic ODEs and SDEs.

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Correspondence to F. S. Nasyrov.

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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).

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  • stochastic differential equation
  • strong solution
  • equation with symmetric integrals
  • ordinary differential equation with random right-hand side
  • Carathéodory solution
  • Filippov solution