We consider symmetric Markov chains on the integer lattice that possibly have arbitrarily large jumps. In the literature, it is proven that under certain conditions, a central limit theorem for a sequence of normalized symmetric Markov chains can be established. In this thesis we calculate an (almost polynomial) rate of convergence through techniques that give bounds on the difference of semigroups.
In the second part of the thesis, we establish the derivative concept for a large class of stochastic flows. We prove that, under certain differentiability conditions on the integrands in a stochastic differential equation, the derivatives of these processes have a version that is continuous from the right and with limits from the left and are continuous in space, and have moments of all orders. A Taylor expansion is derived as well.
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