Mixing
Local Martingale on $[0,T]$
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What is the definition of a local martingale on $[0,T]?$
I guess the definition should be: $M = (M_t)_{t in [0,T]}$ is a local martingale if there exists a localizing sequence $tau_n$ such that for all $n$ the process $M^{tau_n}$ is a martingale.
A sequence of stopping times $(tau_n)_n$ is a localizing sequence if $P$-almost surely $tau_n leq tau_{n+1}$ and $lim_{n to infty} tau_n = T.$
Is this definition correct?
stochastic-calculus
asked 21 hours ago
White
789
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up vote
1
down vote
favorite
What is the definition of a local martingale on $[0,T]?$
I guess the definition should be: $M = (M_t)_{t in [0,T]}$ is a local martingale if there exists a localizing sequence $tau_n$ such that for all $n$ the process $M^{tau_n}$ is a martingale.
A sequence of stopping times $(tau_n)_n$ is a localizing sequence if $P$-almost surely $tau_n leq tau_{n+1}$ and $lim_{n to infty} tau_n = T.$
Is this definition correct?
stochastic-calculus
asked 21 hours ago
White
789
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
What is the definition of a local martingale on $[0,T]?$
I guess the definition should be: $M = (M_t)_{t in [0,T]}$ is a local martingale if there exists a localizing sequence $tau_n$ such that for all $n$ the process $M^{tau_n}$ is a martingale.
A sequence of stopping times $(tau_n)_n$ is a localizing sequence if $P$-almost surely $tau_n leq tau_{n+1}$ and $lim_{n to infty} tau_n = T.$
Is this definition correct?
stochastic-calculus
asked 21 hours ago
White
789
What is the definition of a local martingale on $[0,T]?$
I guess the definition should be: $M = (M_t)_{t in [0,T]}$ is a local martingale if there exists a localizing sequence $tau_n$ such that for all $n$ the process $M^{tau_n}$ is a martingale.
A sequence of stopping times $(tau_n)_n$ is a localizing sequence if $P$-almost surely $tau_n leq tau_{n+1}$ and $lim_{n to infty} tau_n = T.$
Is this definition correct?
stochastic-calculus
stochastic-calculus
asked 21 hours ago
White
789
asked 21 hours ago
White
789
asked 21 hours ago
White
789
asked 21 hours ago
White
789
asked 21 hours ago
White
789
789
add a comment |
add a comment |
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