Invariance Principles for Recursive Residuals

Invariance Principles for Recursive Residuals

Strong Invariance Principles for Sequential

Rafa l Kulik of University of Sydney and Wroc law University has brought to our attention that Assumption A does not help in the proof of our Proposition 2.2, for what is really used in our method of proof is, actually, the uniform boundedness of Jτ (y) and that of its derivatives. However, ifXi = ηi (cf. Remark 2.1), then J1(y) =−φ(Φ −1(y)), and thus, we have J ′ 1(y) =−Φ −1(y), J ′′ 1 (y) = −...

Invariance Principles for Parabolic Equations with Random Coeecients Invariance Principles for Parabolic Equations with Random Coeecients

A general Hilbert-space-based stochastic averaging theory is brought forth in this note for arbitrary-order parabolic equations with (possibly long range dependent) random coeecients. We start with regularity conditions on the coeecients and Cauchy data of @ t u " (x; t) = X 0jkjj2p A k (x; t="; !)@ k x u " (x; t); u " (x; 0) = '(x) (1) which are only slightly stronger than those required to pr...

Group invariance principles for causal generative models

The postulate of independence of cause and mechanism (ICM) has recently led to several new causal discovery algorithms. The interpretation of independence and the way it is utilized, however, varies across these methods. Our aim in this paper is to propose a group theoretic framework for ICM to unify and generalize these approaches. In our setting, the cause-mechanism relationship is assessed b...

Generalized invariance principles for switched delay systems

In many applications, the physical processes are governed by more than one dynamics in which the dynamic changes among a family of choices depending on the time t or the state x . Such processes are often described by switched systems or more generally hybrid systems, which have been studied extensively in recent years (see Goebel et al., 2009; Liberzon, 2003; Shorten et al., 2007; van der Scha...