Moments of a linear stochatic dynamical system
$begingroup$
$X_k in mathrm{R}^n$ is a random variable whose evolution at time $k+1$ is governed by the following equation:
begin{equation}
X_{k+1} = AX_x + Beta_k \
eta_k sim mathcal{N}(0,Sigma)
end{equation}
where, $A$ and $B$ are a time invariant matrices. and $eta_k$ is Gaussian white noise.
If the mean of $X_k$ is represented by $mu_k$, and covariance by $P_k$, then which of the following statements is correct:
$mu_{k+1}$ is exactly equal to $Amu_k$. $P_{k+1}$ is exactly equal to $AP_kA^T + BSigma B^T$.- Estimate of $mu_{k+1}$ is $Amu_k$. Estimate of $P_{k+1}$ is $AP_kA^T + BSigma B^T$.
probability probability-theory stochastic-processes
edited Jan 3 at 14:43
Davide Giraudo
127k16152266
asked Jan 3 at 0:01
user146290user146290
507314
$endgroup$
add a comment |
$begingroup$
$X_k in mathrm{R}^n$ is a random variable whose evolution at time $k+1$ is governed by the following equation:
begin{equation}
X_{k+1} = AX_x + Beta_k \
eta_k sim mathcal{N}(0,Sigma)
end{equation}
where, $A$ and $B$ are a time invariant matrices. and $eta_k$ is Gaussian white noise.
If the mean of $X_k$ is represented by $mu_k$, and covariance by $P_k$, then which of the following statements is correct:
$mu_{k+1}$ is exactly equal to $Amu_k$. $P_{k+1}$ is exactly equal to $AP_kA^T + BSigma B^T$.- Estimate of $mu_{k+1}$ is $Amu_k$. Estimate of $P_{k+1}$ is $AP_kA^T + BSigma B^T$.
probability probability-theory stochastic-processes
edited Jan 3 at 14:43
Davide Giraudo
127k16152266
asked Jan 3 at 0:01
user146290user146290
507314
$endgroup$
add a comment |
$begingroup$
$X_k in mathrm{R}^n$ is a random variable whose evolution at time $k+1$ is governed by the following equation:
begin{equation}
X_{k+1} = AX_x + Beta_k \
eta_k sim mathcal{N}(0,Sigma)
end{equation}
where, $A$ and $B$ are a time invariant matrices. and $eta_k$ is Gaussian white noise.
If the mean of $X_k$ is represented by $mu_k$, and covariance by $P_k$, then which of the following statements is correct:
$mu_{k+1}$ is exactly equal to $Amu_k$. $P_{k+1}$ is exactly equal to $AP_kA^T + BSigma B^T$.- Estimate of $mu_{k+1}$ is $Amu_k$. Estimate of $P_{k+1}$ is $AP_kA^T + BSigma B^T$.
probability probability-theory stochastic-processes
edited Jan 3 at 14:43
Davide Giraudo
127k16152266
asked Jan 3 at 0:01
user146290user146290
507314
$endgroup$
$X_k in mathrm{R}^n$ is a random variable whose evolution at time $k+1$ is governed by the following equation:
begin{equation}
X_{k+1} = AX_x + Beta_k \
eta_k sim mathcal{N}(0,Sigma)
end{equation}
where, $A$ and $B$ are a time invariant matrices. and $eta_k$ is Gaussian white noise.
If the mean of $X_k$ is represented by $mu_k$, and covariance by $P_k$, then which of the following statements is correct:
$mu_{k+1}$ is exactly equal to $Amu_k$. $P_{k+1}$ is exactly equal to $AP_kA^T + BSigma B^T$.- Estimate of $mu_{k+1}$ is $Amu_k$. Estimate of $P_{k+1}$ is $AP_kA^T + BSigma B^T$.
probability probability-theory stochastic-processes
probability probability-theory stochastic-processes
edited Jan 3 at 14:43
Davide Giraudo
127k16152266
asked Jan 3 at 0:01
user146290user146290
507314
edited Jan 3 at 14:43
Davide Giraudo
127k16152266
asked Jan 3 at 0:01
user146290user146290
507314
edited Jan 3 at 14:43
Davide Giraudo
127k16152266
edited Jan 3 at 14:43
Davide Giraudo
127k16152266
edited Jan 3 at 14:43
Davide Giraudo
127k16152266
127k16152266
asked Jan 3 at 0:01
user146290user146290
507314
asked Jan 3 at 0:01
user146290user146290
507314
asked Jan 3 at 0:01
user146290user146290
507314
507314
add a comment |
add a comment |
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