Mixing
Using Itō's formula to solve a differential equation
$begingroup$
Hi I am struggling on a past question in a previous stochastic calculus exam paper where we are considering the process $Z=(Z_{t})$ defined by
$Z_{t}=sqrt{sqrt{2t}e^{-sqrt{2t}}}times B_{e^{sqrt{2t}}-1}$
and we are told to show by Ito's formula that Z solves the stochastic differential equation
$dZ_{t}=f(t)Z_{t}dt+dM_{t}$ with $(Z_{0}=0)$.
Where we are told to determine the function f explicity.
We also have a stochastic process M which we have previously shown to be a standard Brownian motion in the first part of our question and is defined by:
$M_t=int_0^{e^{sqrt{2t}-1}} sqrt{frac{log(1+s)}{1+s}}dB_s$
Not sure where to start with it and what to apply ito's formula to any help would be appreciated, thank you
stochastic-calculus
edited Jan 11 at 19:41
Bernard
120k740116
asked Jan 11 at 19:37
maxmax
11
$endgroup$
|
show 3 more comments
$begingroup$
Hi I am struggling on a past question in a previous stochastic calculus exam paper where we are considering the process $Z=(Z_{t})$ defined by
$Z_{t}=sqrt{sqrt{2t}e^{-sqrt{2t}}}times B_{e^{sqrt{2t}}-1}$
and we are told to show by Ito's formula that Z solves the stochastic differential equation
$dZ_{t}=f(t)Z_{t}dt+dM_{t}$ with $(Z_{0}=0)$.
Where we are told to determine the function f explicity.
We also have a stochastic process M which we have previously shown to be a standard Brownian motion in the first part of our question and is defined by:
$M_t=int_0^{e^{sqrt{2t}-1}} sqrt{frac{log(1+s)}{1+s}}dB_s$
Not sure where to start with it and what to apply ito's formula to any help would be appreciated, thank you
stochastic-calculus
edited Jan 11 at 19:41
Bernard
120k740116
asked Jan 11 at 19:37
maxmax
11
$endgroup$
$begingroup$
That's the third time that you are asking this question, isn't it? Or perhaps already the 4th time...?
$endgroup$
– saz
Jan 11 at 19:39
$begingroup$
You're a bundle of fun aren't you, thank you for the helpful comment! @saz
$endgroup$
– max
Jan 11 at 21:57
$begingroup$
I left you a helpful comment last time when you asked this question... you obviously chose to ignore it.
$endgroup$
– saz
Jan 12 at 7:55
$begingroup$
You pointed out mistakes in my upload and made no attempt to help solve my problem just as you are doing now. If you have any idea how to solve this question then feel free to comment, if not go and find something better to do with your time. @saz
$endgroup$
– max
Jan 12 at 9:33
$begingroup$
The first time you posted it I was asking about a clarification regarding $M$ and $f$ (since you didn't explain what they are). The second time you posted it, I gave you a hint. But yes, I will follow your suggestion and do something better with my time. Re-posting questions without showing any effort doesn't do you any good.
$endgroup$
– saz
Jan 12 at 9:49
|
show 3 more comments
$begingroup$
Hi I am struggling on a past question in a previous stochastic calculus exam paper where we are considering the process $Z=(Z_{t})$ defined by
$Z_{t}=sqrt{sqrt{2t}e^{-sqrt{2t}}}times B_{e^{sqrt{2t}}-1}$
and we are told to show by Ito's formula that Z solves the stochastic differential equation
$dZ_{t}=f(t)Z_{t}dt+dM_{t}$ with $(Z_{0}=0)$.
Where we are told to determine the function f explicity.
We also have a stochastic process M which we have previously shown to be a standard Brownian motion in the first part of our question and is defined by:
$M_t=int_0^{e^{sqrt{2t}-1}} sqrt{frac{log(1+s)}{1+s}}dB_s$
Not sure where to start with it and what to apply ito's formula to any help would be appreciated, thank you
stochastic-calculus
edited Jan 11 at 19:41
Bernard
120k740116
asked Jan 11 at 19:37
maxmax
11
$endgroup$
Hi I am struggling on a past question in a previous stochastic calculus exam paper where we are considering the process $Z=(Z_{t})$ defined by
$Z_{t}=sqrt{sqrt{2t}e^{-sqrt{2t}}}times B_{e^{sqrt{2t}}-1}$
and we are told to show by Ito's formula that Z solves the stochastic differential equation
$dZ_{t}=f(t)Z_{t}dt+dM_{t}$ with $(Z_{0}=0)$.
Where we are told to determine the function f explicity.
We also have a stochastic process M which we have previously shown to be a standard Brownian motion in the first part of our question and is defined by:
$M_t=int_0^{e^{sqrt{2t}-1}} sqrt{frac{log(1+s)}{1+s}}dB_s$
Not sure where to start with it and what to apply ito's formula to any help would be appreciated, thank you
stochastic-calculus
stochastic-calculus
edited Jan 11 at 19:41
Bernard
120k740116
asked Jan 11 at 19:37
maxmax
11
edited Jan 11 at 19:41
Bernard
120k740116
asked Jan 11 at 19:37
maxmax
11
edited Jan 11 at 19:41
Bernard
120k740116
edited Jan 11 at 19:41
Bernard
120k740116
edited Jan 11 at 19:41
Bernard
120k740116
120k740116
asked Jan 11 at 19:37
maxmax
11
asked Jan 11 at 19:37
maxmax
11
asked Jan 11 at 19:37
maxmax
11
11
$begingroup$
That's the third time that you are asking this question, isn't it? Or perhaps already the 4th time...?
$endgroup$
– saz
Jan 11 at 19:39
$begingroup$
You're a bundle of fun aren't you, thank you for the helpful comment! @saz
$endgroup$
– max
Jan 11 at 21:57
$begingroup$
I left you a helpful comment last time when you asked this question... you obviously chose to ignore it.
$endgroup$
– saz
Jan 12 at 7:55
$begingroup$
You pointed out mistakes in my upload and made no attempt to help solve my problem just as you are doing now. If you have any idea how to solve this question then feel free to comment, if not go and find something better to do with your time. @saz
$endgroup$
– max
Jan 12 at 9:33
$begingroup$
The first time you posted it I was asking about a clarification regarding $M$ and $f$ (since you didn't explain what they are). The second time you posted it, I gave you a hint. But yes, I will follow your suggestion and do something better with my time. Re-posting questions without showing any effort doesn't do you any good.
$endgroup$
– saz
Jan 12 at 9:49
|
show 3 more comments
$begingroup$
That's the third time that you are asking this question, isn't it? Or perhaps already the 4th time...?
$endgroup$
– saz
Jan 11 at 19:39
$begingroup$
You're a bundle of fun aren't you, thank you for the helpful comment! @saz
$endgroup$
– max
Jan 11 at 21:57
$begingroup$
I left you a helpful comment last time when you asked this question... you obviously chose to ignore it.
$endgroup$
– saz
Jan 12 at 7:55
$begingroup$
You pointed out mistakes in my upload and made no attempt to help solve my problem just as you are doing now. If you have any idea how to solve this question then feel free to comment, if not go and find something better to do with your time. @saz
$endgroup$
– max
Jan 12 at 9:33
$begingroup$
The first time you posted it I was asking about a clarification regarding $M$ and $f$ (since you didn't explain what they are). The second time you posted it, I gave you a hint. But yes, I will follow your suggestion and do something better with my time. Re-posting questions without showing any effort doesn't do you any good.
$endgroup$
– saz
Jan 12 at 9:49
$begingroup$
That's the third time that you are asking this question, isn't it? Or perhaps already the 4th time...?
$endgroup$
– saz
Jan 11 at 19:39
$begingroup$
That's the third time that you are asking this question, isn't it? Or perhaps already the 4th time...?
$endgroup$
– saz
Jan 11 at 19:39
$begingroup$
You're a bundle of fun aren't you, thank you for the helpful comment! @saz
$endgroup$
– max
Jan 11 at 21:57
$begingroup$
You're a bundle of fun aren't you, thank you for the helpful comment! @saz
$endgroup$
– max
Jan 11 at 21:57
$begingroup$
I left you a helpful comment last time when you asked this question... you obviously chose to ignore it.
$endgroup$
– saz
Jan 12 at 7:55
$begingroup$
I left you a helpful comment last time when you asked this question... you obviously chose to ignore it.
$endgroup$
– saz
Jan 12 at 7:55
$begingroup$
You pointed out mistakes in my upload and made no attempt to help solve my problem just as you are doing now. If you have any idea how to solve this question then feel free to comment, if not go and find something better to do with your time. @saz
$endgroup$
– max
Jan 12 at 9:33
$begingroup$
You pointed out mistakes in my upload and made no attempt to help solve my problem just as you are doing now. If you have any idea how to solve this question then feel free to comment, if not go and find something better to do with your time. @saz
$endgroup$
– max
Jan 12 at 9:33
$begingroup$
The first time you posted it I was asking about a clarification regarding $M$ and $f$ (since you didn't explain what they are). The second time you posted it, I gave you a hint. But yes, I will follow your suggestion and do something better with my time. Re-posting questions without showing any effort doesn't do you any good.
$endgroup$
– saz
Jan 12 at 9:49
$begingroup$
The first time you posted it I was asking about a clarification regarding $M$ and $f$ (since you didn't explain what they are). The second time you posted it, I gave you a hint. But yes, I will follow your suggestion and do something better with my time. Re-posting questions without showing any effort doesn't do you any good.
$endgroup$
– saz
Jan 12 at 9:49
|
show 3 more comments
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$begingroup$
That's the third time that you are asking this question, isn't it? Or perhaps already the 4th time...?
$endgroup$
– saz
Jan 11 at 19:39
$begingroup$
You're a bundle of fun aren't you, thank you for the helpful comment! @saz
$endgroup$
– max
Jan 11 at 21:57
$begingroup$
I left you a helpful comment last time when you asked this question... you obviously chose to ignore it.
$endgroup$
– saz
Jan 12 at 7:55
$begingroup$
You pointed out mistakes in my upload and made no attempt to help solve my problem just as you are doing now. If you have any idea how to solve this question then feel free to comment, if not go and find something better to do with your time. @saz
$endgroup$
– max
Jan 12 at 9:33
$begingroup$
The first time you posted it I was asking about a clarification regarding $M$ and $f$ (since you didn't explain what they are). The second time you posted it, I gave you a hint. But yes, I will follow your suggestion and do something better with my time. Re-posting questions without showing any effort doesn't do you any good.
$endgroup$
– saz
Jan 12 at 9:49