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Stochastic calculus provides a consistent theory of integration for stochastic processes and is used to model random systems. Its applications range from statistical physics to quantitative finance.
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How to show a space is an invariant core for a strongly continuous semigroup?
This question comes from a paper 2015(Kolokoltsov) Theorem 4.1.
In the end of the proof i), “Applying to $T_t$ the procedure applied above to $T_t^h$ shows that $T_t$ defines also a strongly continuou …
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How to understand the transition density of reflected Brownian motion
We can see from the above picture the transition density of reflecting Browninan motion is given by (19). As we know, the first part ($2p(t,x,y)$) is the transition density of a Brownian motion (from …