Limit Theorems for Stochastic Processes |
Contents
The General Theory of Stochastic Processes | 1 |
Convergence of Stochastic Integrals | 5 |
Predictable σField Predictable Times | 17 |
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A₁ absolute continuity adapted process Aloc assume B₁ belongs C₁ cądląg cądląg 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