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The law of Euler scheme for stochastic differential equations: convergence rate of the density. Partial differential equations of
We show how to use the Malliavin calculus to obtain a new exact formula for the density ρ of the law of any random variable Z which is measurable and differentiable with respect to
Keywords: Adaptive Markov chains, Coupling, Markov Chain Monte Carlo, Metropolis Algo- rithm, Stochastic Approximation, Rate of
Key words: stochastic differential equations, Brownian motion, Law of the Iterated Logarithm, Motoo’s theorem, stochastic comparison principle, stationary processes,
Although conditions (conditions UCV and UT) to ensure that one may interchange lim- its and stochastic integrals driven by semimartingales are now well known, the problem
Key words: Central Limit Theorems; Malliavin calculus; Multi-dimensional normal approxi- mations; Ornstein-Uhlenbeck processes; Poisson measures; Probabilistic Interpolations;
Key words: semimartingales; Gaussian processes; stationary processes; moving averages; stochastic convolutions; non-canonical representations.. AMS 2000 Subject Classification:
Keywords: Total variation distance; Non-central limit theorem; Fractional Brownian motion; Hermite power variation; Multiple stochastic integrals; Hermite random