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What is the distribution of $dX_t = bsigma_tdV_t$?

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0

$begingroup$

$$dX_t =sigma_tX^a dW_t$$
$$dsigma_t = bsigma_tdV_t$$
$$ dV_tdW_t = rho dt$$

$V,W$ are two correlated Brownian Motions. $a$ and $b$ is two real valued parameters. If $X_0$, $sigma_0$, a, b and $rho$ is known: What are the distribution of $X_t$?

$sigma_t$ is a Geometric Brownian motion with no drift.

probability probability-theory probability-distributions stochastic-processes stochastic-calculus

share|cite|improve this question

edited Mar 13 at 12:09

k.dkhk

asked Mar 12 at 5:19

k.dkhkk.dkhk

16410

$endgroup$

add a comment | 

0

$begingroup$

$$dX_t =sigma_tX^a dW_t$$
$$dsigma_t = bsigma_tdV_t$$
$$ dV_tdW_t = rho dt$$

$V,W$ are two correlated Brownian Motions. $a$ and $b$ is two real valued parameters. If $X_0$, $sigma_0$, a, b and $rho$ is known: What are the distribution of $X_t$?

$sigma_t$ is a Geometric Brownian motion with no drift.

probability probability-theory probability-distributions stochastic-processes stochastic-calculus

share|cite|improve this question

edited Mar 13 at 12:09

k.dkhk

asked Mar 12 at 5:19

k.dkhkk.dkhk

16410

$endgroup$

add a comment | 

$begingroup$

$$dX_t =sigma_tX^a dW_t$$
$$dsigma_t = bsigma_tdV_t$$
$$ dV_tdW_t = rho dt$$

$V,W$ are two correlated Brownian Motions. $a$ and $b$ is two real valued parameters. If $X_0$, $sigma_0$, a, b and $rho$ is known: What are the distribution of $X_t$?

$sigma_t$ is a Geometric Brownian motion with no drift.

probability probability-theory probability-distributions stochastic-processes stochastic-calculus

share|cite|improve this question

edited Mar 13 at 12:09

k.dkhk

asked Mar 12 at 5:19

k.dkhkk.dkhk

16410

$endgroup$

share|cite|improve this question

edited Mar 13 at 12:09

k.dkhk

asked Mar 12 at 5:19

k.dkhkk.dkhk

16410

share|cite|improve this question

edited Mar 13 at 12:09

k.dkhk

asked Mar 12 at 5:19

k.dkhkk.dkhk

16410

asked Mar 12 at 5:19

k.dkhkk.dkhk

16410

asked Mar 12 at 5:19

k.dkhkk.dkhk

16410