Limit Theorems for Stochastic Processes |
From inside the book
Results 1-3 of 78
Page 376
... fixed time of discontinuity , the claim is a ( weaker ) version of the necessary part of 2.59 . 66799 b ) Conversely ... fixed times of discontinuity , then X also has no fixed time of discontinuity . Proof . The assumption implies that ...
... fixed time of discontinuity , the claim is a ( weaker ) version of the necessary part of 2.59 . 66799 b ) Conversely ... fixed times of discontinuity , then X also has no fixed time of discontinuity . Proof . The assumption implies that ...
Page 421
... fixed and let ( n ' ) be an infinite subsequence . By a diagonal argument , there is a further subsequence ( n " ) and a set A with P ( A ) = 1 , such that sup yn " s < t ' ( w ; { s } × { | x | > ε } ) → 0 for all & > 0 Br ...
... fixed and let ( n ' ) be an infinite subsequence . By a diagonal argument , there is a further subsequence ( n " ) and a set A with P ( A ) = 1 , such that sup yn " s < t ' ( w ; { s } × { | x | > ε } ) → 0 for all & > 0 Br ...
Page 426
... fixed time of discontinuity , with characteristics ( B , C , v ) . If B , 5 , ΣE " [ h ( U ) F - 1 ] - B0 for all t ... fixed time of discontinuity . If 2.31 then XnX . 2.32 sup sup | G " ( u ) , − g ( u ) , | 0 for all t > 0 , 0 > 0 ...
... fixed time of discontinuity , with characteristics ( B , C , v ) . If B , 5 , ΣE " [ h ( U ) F - 1 ] - B0 for all t ... fixed time of discontinuity . If 2.31 then XnX . 2.32 sup sup | G " ( u ) , − g ( u ) , | 0 for all t > 0 , 0 > 0 ...
Contents
The General Theory of Stochastic Processes | 1 |
Convergence of Stochastic Integrals | 5 |
Predictable σField Predictable Times | 17 |
Copyright | |
48 other sections not shown
Other editions - View all
Common terms and phrases
A₁ absolute continuity adapted process Aloc assume B₁ belongs C₁ càdlàg càdlàg adapted canonical characteristics compensator condition continuous convergence Corollary d-dimensional decomposition deduce defined definition denote density process deterministic equivalence evanescent set exists filtration finite variation follows Hellinger process hence holds implies increasing process independent increments inf(t jumps Lemma lim sup local martingale locally bounded martingale problem Moreover nonnegative notation o-field obtain obvious P-local martingale P-measurable point process Poisson process predictable process probability measure process H Proof Proposition purely discontinuous random set random variables recall remains to prove resp result S₁ satisfies semimartingale Skorokhod topology space square-integrable stochastic basis stochastic integral strict stopping subsection T₁ topology trivial truncation function uniformly integrable uniqueness Var(A Wiener process X|PH X₁ yields Z₁