Order in probability of a ratio between two integrals
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Suppose that $mu$ is an adapted bounded stochastic process and suppose that $sigma$ is an adapted bounded left-continuous stochastic process. I want to prove that
$$
frac{int_0^{Delta}mu_s,ds}{int_0^{Delta}sigma_s,dW_s}=O_pleft(sqrt{Delta}right)
$$
The idea is that, since $int_0^{Delta}mu_s,ds=O_p(Delta)$ and $int_0^{Delta}sigma_s,dW_s=O_pleft(sqrt{Delta}right)$ then the ratio should be $O_pleft(frac{Delta}{sqrt{Delta}}right)=O_pleft(sqrt{Delta}right)$.
stochastic-processes asymptotics stochastic-integrals
asked Nov 19 at 14:41
AlmostSureUser
307417
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up vote
0
down vote
favorite
Suppose that $mu$ is an adapted bounded stochastic process and suppose that $sigma$ is an adapted bounded left-continuous stochastic process. I want to prove that
$$
frac{int_0^{Delta}mu_s,ds}{int_0^{Delta}sigma_s,dW_s}=O_pleft(sqrt{Delta}right)
$$
The idea is that, since $int_0^{Delta}mu_s,ds=O_p(Delta)$ and $int_0^{Delta}sigma_s,dW_s=O_pleft(sqrt{Delta}right)$ then the ratio should be $O_pleft(frac{Delta}{sqrt{Delta}}right)=O_pleft(sqrt{Delta}right)$.
stochastic-processes asymptotics stochastic-integrals
asked Nov 19 at 14:41
AlmostSureUser
307417
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose that $mu$ is an adapted bounded stochastic process and suppose that $sigma$ is an adapted bounded left-continuous stochastic process. I want to prove that
$$
frac{int_0^{Delta}mu_s,ds}{int_0^{Delta}sigma_s,dW_s}=O_pleft(sqrt{Delta}right)
$$
The idea is that, since $int_0^{Delta}mu_s,ds=O_p(Delta)$ and $int_0^{Delta}sigma_s,dW_s=O_pleft(sqrt{Delta}right)$ then the ratio should be $O_pleft(frac{Delta}{sqrt{Delta}}right)=O_pleft(sqrt{Delta}right)$.
stochastic-processes asymptotics stochastic-integrals
asked Nov 19 at 14:41
AlmostSureUser
307417
Suppose that $mu$ is an adapted bounded stochastic process and suppose that $sigma$ is an adapted bounded left-continuous stochastic process. I want to prove that
$$
frac{int_0^{Delta}mu_s,ds}{int_0^{Delta}sigma_s,dW_s}=O_pleft(sqrt{Delta}right)
$$
The idea is that, since $int_0^{Delta}mu_s,ds=O_p(Delta)$ and $int_0^{Delta}sigma_s,dW_s=O_pleft(sqrt{Delta}right)$ then the ratio should be $O_pleft(frac{Delta}{sqrt{Delta}}right)=O_pleft(sqrt{Delta}right)$.
stochastic-processes asymptotics stochastic-integrals
stochastic-processes asymptotics stochastic-integrals
asked Nov 19 at 14:41
AlmostSureUser
307417
asked Nov 19 at 14:41
AlmostSureUser
307417
asked Nov 19 at 14:41
AlmostSureUser
307417
asked Nov 19 at 14:41
AlmostSureUser
307417
asked Nov 19 at 14:41
AlmostSureUser
307417
307417
add a comment |
add a comment |
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