Increasing process
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An increasing process is a stochastic process... : (X_t)_{t \in M} ...where the random variables X_t which make up the process are increasing almost surely and adapted: : 0=X_0 \leq X_{t_1} \leq \cdots . A continuous increasing process is such a process where the set M is continuous. Consider a stochastic process (\Chi_t) satisfying X_t \leq X_s a.s. for all t \leq s My question is: Does there exist a modification \breve{X} of , X which almost surely has increasing sample paths t \mapsto \breve{X}_t(\omega) ?
An increasing process is a stochastic process... (X_t)_{t \in M} ...where the random variables X_t which make up the process are increasing almost surely and adapted: 0=X_0 \leq X_{t_1} \leq \cdots . A continuous increasing process is such a process where the set M is continuous. Consider a stochastic process (\Chi_t) satisfying X_t \leq X_s a.s. for all t \leq s My question is: Does there exist a modification \breve{X} of , X which almost surely has increasing sample paths t \mapsto \breve{X}_t(\omega) ? ==References==
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