Mixing
comparison of two stochastic processes
$begingroup$
Let $(Omega, mathcal{F}, P, mathcal{F}_t)$ be a probability space under "usual conditions" and two semimartingales X and Y such that
$$X=W_t+I_{(hleq1)}h(omega,t,X,u)*(mu-nu)_t+I_{(hleq1)}(h(omega,t,X,u)-f(omega,t,X,u))*nu_t$$
$$Y=W_t+I_{(kleq1)}k(omega,t,Y,u)*(mu-nu)_t+I_{(kleq1)}(k(omega,t,Y,u)-g(omega,t,Y,u))*nu_t$$
where W is a wiener process, $mu$ is integer valued jump measure and $nu$ its compensator.
My ultimate goal to compare this 2 processes.
To apply a formula of change of variables to the given processes I need to rewrite the processes in canonical form. So I need to somehow decompose compensator $nu$ because it is not included in the canonical form.
How is it possible to decompose $nu$?
or may be there are any already proved theorems for processes with different jump coefficients? (I didn't find any good sources)
stochastic-analysis sde
asked Jan 24 at 20:48
Andrey PakAndrey Pak
788
$endgroup$
add a comment |
$begingroup$
Let $(Omega, mathcal{F}, P, mathcal{F}_t)$ be a probability space under "usual conditions" and two semimartingales X and Y such that
$$X=W_t+I_{(hleq1)}h(omega,t,X,u)*(mu-nu)_t+I_{(hleq1)}(h(omega,t,X,u)-f(omega,t,X,u))*nu_t$$
$$Y=W_t+I_{(kleq1)}k(omega,t,Y,u)*(mu-nu)_t+I_{(kleq1)}(k(omega,t,Y,u)-g(omega,t,Y,u))*nu_t$$
where W is a wiener process, $mu$ is integer valued jump measure and $nu$ its compensator.
My ultimate goal to compare this 2 processes.
To apply a formula of change of variables to the given processes I need to rewrite the processes in canonical form. So I need to somehow decompose compensator $nu$ because it is not included in the canonical form.
How is it possible to decompose $nu$?
or may be there are any already proved theorems for processes with different jump coefficients? (I didn't find any good sources)
stochastic-analysis sde
asked Jan 24 at 20:48
Andrey PakAndrey Pak
788
$endgroup$
add a comment |
$begingroup$
Let $(Omega, mathcal{F}, P, mathcal{F}_t)$ be a probability space under "usual conditions" and two semimartingales X and Y such that
$$X=W_t+I_{(hleq1)}h(omega,t,X,u)*(mu-nu)_t+I_{(hleq1)}(h(omega,t,X,u)-f(omega,t,X,u))*nu_t$$
$$Y=W_t+I_{(kleq1)}k(omega,t,Y,u)*(mu-nu)_t+I_{(kleq1)}(k(omega,t,Y,u)-g(omega,t,Y,u))*nu_t$$
where W is a wiener process, $mu$ is integer valued jump measure and $nu$ its compensator.
My ultimate goal to compare this 2 processes.
To apply a formula of change of variables to the given processes I need to rewrite the processes in canonical form. So I need to somehow decompose compensator $nu$ because it is not included in the canonical form.
How is it possible to decompose $nu$?
or may be there are any already proved theorems for processes with different jump coefficients? (I didn't find any good sources)
stochastic-analysis sde
asked Jan 24 at 20:48
Andrey PakAndrey Pak
788
$endgroup$
Let $(Omega, mathcal{F}, P, mathcal{F}_t)$ be a probability space under "usual conditions" and two semimartingales X and Y such that
$$X=W_t+I_{(hleq1)}h(omega,t,X,u)*(mu-nu)_t+I_{(hleq1)}(h(omega,t,X,u)-f(omega,t,X,u))*nu_t$$
$$Y=W_t+I_{(kleq1)}k(omega,t,Y,u)*(mu-nu)_t+I_{(kleq1)}(k(omega,t,Y,u)-g(omega,t,Y,u))*nu_t$$
where W is a wiener process, $mu$ is integer valued jump measure and $nu$ its compensator.
My ultimate goal to compare this 2 processes.
To apply a formula of change of variables to the given processes I need to rewrite the processes in canonical form. So I need to somehow decompose compensator $nu$ because it is not included in the canonical form.
How is it possible to decompose $nu$?
or may be there are any already proved theorems for processes with different jump coefficients? (I didn't find any good sources)
stochastic-analysis sde
stochastic-analysis sde
asked Jan 24 at 20:48
Andrey PakAndrey Pak
788
asked Jan 24 at 20:48
Andrey PakAndrey Pak
788
asked Jan 24 at 20:48
Andrey PakAndrey Pak
788
asked Jan 24 at 20:48
Andrey PakAndrey Pak
788
asked Jan 24 at 20:48
Andrey PakAndrey Pak
788
788
add a comment |
add a comment |
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