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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

17 votes
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Correlated Brownian motion and Poisson process

You can not construct a Poisson process $N$, and a Brownian motion $W$ on the same filtration such that they are dependent. They are always independent on the given filtration. Let $(W_t)_{t\geq 0}$ …
kakuritsu's user avatar
  • 328
4 votes
1 answer
495 views

Correlation structure among the maximums of a Brownian motion

Is there a known correlation structure among the maximums of a Brownian motion on disjoint intervals ? Let $(W_t)_{t\geq 0}$ be a one-dimensional standard Brownian motion, and take the partition $0 …
kakuritsu's user avatar
  • 328