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 Nov 19 at 10:46
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 Nov 19 at 10:46
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 Nov 19 at 10:46
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 Nov 19 at 10:46
White
789
asked Nov 19 at 10:46
White
789
asked Nov 19 at 10:46
White
789
asked Nov 19 at 10:46
White
789
asked Nov 19 at 10:46
White
789
789
add a comment |
add a comment |
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