Convergence en loi des suites d'intégrales stochastiques sur l'espace $$\mathbb{D}$$ 1 de Skorokhod

Convergence in Dirichlet Law of Certain Stochastic Integrals

“…Since the process X n is a continuous semi-martingale, quiet general conditions, depending on the regularity of h, may be found in the literature. When h is càd-làg (right continuous with left limit), a sufficient condition for X n is to satisfy the so-called U.T criterium proved by Jakubowski, Mémin and Pagès (cf [14] or [16] for an equivalent formulation). Since X n is a finite variation process, according to the proposition 6.12 p.378 of [13], the U.T condition is equivalent to the tightness of the sequence (V ar(X n ) t ) n∈N * , for all t ∈ [0, 1], V ar(X n ) being the variation process given by…”

On approximation of stochastic differential equations with coefficients depending on the past

“…Therefore, from the condition 3 in Definition 2 we have that the total variations [Aij (X 6) IT are also uniformly bounded for each T. Now, after the reductions made, we easily see that in (9) Proof. The lemma follows, for example, from general results of Jakubowski-M6min-Pag~s [8]. See also [3], Lemma on p. 348, [13], Proposition 2.3.4.…”

Asymptotic behavior of the multilevel type error for SDEs driven by a pure jump Lévy process

“…Uniformly tight processes. We recall the definition of uniformly tight property (U T ) defined in Jakubowski, Mémin and Pagès (1989) [13]. Let Z n be a sequence of semimartingale, with the canonical decompositions…”