Dynkin formula and expectation
$begingroup$
I have a question about the use of Dynkin's formula. Suppose I have a stochastic process $X_t$, from an SDE that I cannot solve analytically. I want to find the expectation $mathbb{E}X_t$. By Dynkin with initial condition $X_0=x$,
$$mathbb{E}X_t=x+mathbb{E}^xint_0^t L(X_s)ds$$
,here $L$ is the generator of the diffusion, found from the SDE. How would one find an expression for the expectation of the integral?
probability-theory stochastic-processes stochastic-calculus stochastic-integrals sde
edited Dec 16 '18 at 8:58
Davide Giraudo
127k16151264
asked Dec 16 '18 at 1:39
thaumoctopusthaumoctopus
9519
$endgroup$
add a comment |
$begingroup$
I have a question about the use of Dynkin's formula. Suppose I have a stochastic process $X_t$, from an SDE that I cannot solve analytically. I want to find the expectation $mathbb{E}X_t$. By Dynkin with initial condition $X_0=x$,
$$mathbb{E}X_t=x+mathbb{E}^xint_0^t L(X_s)ds$$
,here $L$ is the generator of the diffusion, found from the SDE. How would one find an expression for the expectation of the integral?
probability-theory stochastic-processes stochastic-calculus stochastic-integrals sde
edited Dec 16 '18 at 8:58
Davide Giraudo
127k16151264
asked Dec 16 '18 at 1:39
thaumoctopusthaumoctopus
9519
$endgroup$
add a comment |
$begingroup$
I have a question about the use of Dynkin's formula. Suppose I have a stochastic process $X_t$, from an SDE that I cannot solve analytically. I want to find the expectation $mathbb{E}X_t$. By Dynkin with initial condition $X_0=x$,
$$mathbb{E}X_t=x+mathbb{E}^xint_0^t L(X_s)ds$$
,here $L$ is the generator of the diffusion, found from the SDE. How would one find an expression for the expectation of the integral?
probability-theory stochastic-processes stochastic-calculus stochastic-integrals sde
edited Dec 16 '18 at 8:58
Davide Giraudo
127k16151264
asked Dec 16 '18 at 1:39
thaumoctopusthaumoctopus
9519
$endgroup$
I have a question about the use of Dynkin's formula. Suppose I have a stochastic process $X_t$, from an SDE that I cannot solve analytically. I want to find the expectation $mathbb{E}X_t$. By Dynkin with initial condition $X_0=x$,
$$mathbb{E}X_t=x+mathbb{E}^xint_0^t L(X_s)ds$$
,here $L$ is the generator of the diffusion, found from the SDE. How would one find an expression for the expectation of the integral?
probability-theory stochastic-processes stochastic-calculus stochastic-integrals sde
probability-theory stochastic-processes stochastic-calculus stochastic-integrals sde
edited Dec 16 '18 at 8:58
Davide Giraudo
127k16151264
asked Dec 16 '18 at 1:39
thaumoctopusthaumoctopus
9519
edited Dec 16 '18 at 8:58
Davide Giraudo
127k16151264
asked Dec 16 '18 at 1:39
thaumoctopusthaumoctopus
9519
edited Dec 16 '18 at 8:58
Davide Giraudo
127k16151264
edited Dec 16 '18 at 8:58
Davide Giraudo
127k16151264
edited Dec 16 '18 at 8:58
Davide Giraudo
127k16151264
127k16151264
asked Dec 16 '18 at 1:39
thaumoctopusthaumoctopus
9519
asked Dec 16 '18 at 1:39
thaumoctopusthaumoctopus
9519
asked Dec 16 '18 at 1:39
thaumoctopusthaumoctopus
9519
9519
add a comment |
add a comment |
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