Quadratic Variation: Total Variation, Bounded Variation, Mathematics, Stochastic Process, Wiener Process, Martingale (Probability Theory) - Couverture souple

 
9786130498016: Quadratic Variation: Total Variation, Bounded Variation, Mathematics, Stochastic Process, Wiener Process, Martingale (Probability Theory)

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and martingales. Quadratic variation is just one kind of variation of a process. A process X is said to have finite variation if it is has bounded variation over every finite time interval (with probability 1). Such processes are very common including, in particular, all continuously differentiable functions. The quadratic variation exists for all continuous finite variation processes, and is zero. This statement can be generalized to non-continuous processes. Any càdlàg finite variation process X has quadratic variation equal to the sum of the squares of the jumps of X.

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