A note on comparison theorems for stochastic differential equations with respect to semimartingales

DOI10.1080/17442509108833726zbMath0739.60049OpenAlexW2073686100MaRDI QIDQ3986622

Xuerong Mao

Publication date: 27 June 1992

Published in: Stochastics and Stochastic Reports (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442509108833726

zbMATH Keywords

comparison theoremsemimartingalesstochastic differential equationsLyapunov-like function

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic stability in control theory (93E15)

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Order preservation for path-distribution dependent SDEs ⋮ Periodic solutions of stochastic functional differential equations with jumps via viability ⋮ Comparison theorem for path dependent SDEs driven by G-Brownian motion ⋮ Captive jump processes for bounded random systems with discontinuous dynamics ⋮ Comparison theorem for stochastic differential delay equations with jumps ⋮ Comparison theorem of one-dimensional stochastic hybrid delay systems ⋮ A Necessary condition on comparison theorem for one-dimensional stochastic differential equation ⋮ Order preservation for multidimensional stochastic functional differential equations with jumps ⋮ Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations ⋮ Comparison theorem for distribution-dependent neutral SFDEs ⋮ Distribution dependent stochastic differential equations ⋮ Advances in Stabilization of Hybrid Stochastic Differential Equations by Delay Feedback Control ⋮ Multiple Solutions to Stochastic Differential Delay Equations and a Related Comparison Theorem

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