Asymptotic Methods in the Theory of Stochastic Differential Equations

By A. Skorokhod. 2008

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Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging (2009, background): “2 relies on a powerful result by Skorokhod (Theorem 1 of Chapter II of [108]) stating that the convergence in distribution of a sequence of stochastic processes is implied by the convergence of their generators.”
Elliptic and parabolic equations for measures (2009, neutral): “are considered in [9], [51], [60], [177], [110], [132], [141], [142], [164], [166], [175], [176], [180].”
Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching (2009, background): “It is well-known (see Skorohod [12]) that almost every sample path of r(t) is a right-continuous step functon with a finite number of simple jumps in any finite subinterval of R+.”
Feynman–Kac formulas for regime-switching jump diffusions and their applications (2015, background): “Similar to diffusions, for every f [ DL, a result known as generalized Itô’s lemma (see [37,40,44]) reads”
On competitive Lotka-Volterra model in random environments (2009, background): “(i) It follows from generalized Itô’s Lemma [42] that”
Stability of regime-switching diffusions (2007, background): “3) has a unique solution; see [13] for details.”