XIII: 25, 281-293, LNM 721 (1979)
ÉMERY, Michel
Équations différentielles stochastiques lipschitziennes~: étude de la stabilité (
Stochastic calculus)
This is the main application of the topologies on processes and semimartingales introduced in
1324. Using a very general definition of stochastic differential equations turns out to make the proof much simpler, and the existence and uniqueness of solutions of such equations is proved anew before the stability problem is discussed. Useful inequalities on stochastic integration are proved, and used as technical tools
Comment: For all of this subject, the book of Protter
Stochastic Integration and Differential Equations, Springer 1989, is a useful reference
Keywords: Stochastic differential equations,
StabilityNature: Original
Retrieve article from Numdam
XLV: 07, 181-199, LNM 2078 (2013)
HASHIMOTO, Hiroya
Approximation and Stability of Solutions of SDEs Driven by a Symmetric $\alpha$-Stable Process with Non-Lipschitz Coefficients (
Theory of processes)
Keywords: $\alpha$-stable processes,
Euler-Maruyama approximation,
stability of solutionNature: Original
