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Published in:
2016 | OriginalPaper | Chapter
On the Markov Property
Author : René Schilling
Published in: From Lévy-Type Processes to Parabolic SPDEs
Publisher: Springer International Publishing
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Let $$ \left( {\Omega, \,\mathcal{A},\,\mathbb{P}} \right) $$ be a probability space with some filtration $$ \left( {\mathcal{F}_t } \right)_{t \geqslant 0} $$ and a d-dimensional adapted stochastic process $$ X = \left( {X_t } \right)_{t \geqslant 0} $$ , i.e., each Xt is $$ \mathcal{F}_t $$ measurable.We write $$ \mathcal{B}\left( {\mathbb{R}^d } \right) $$ for the Borel sets and set $$ F_\infty : = \sigma \left( { \cup _{t \geqslant 0} F_t} \right) $$ .