Expected Value of an expression including error function
$begingroup$
I want to calculate the expected value to the solution of a Fokker-Plank equation, so one of the terms I got includes the complementary error function, namely:
$$p(x,t|x_{0},t_{0})=frac{B}{2 D}*e^{frac{-Bx}{D}} * erfc(frac{x+x_{0}-Bt}{2sqrt{Dt}})$$
So my question is, while calculating the intergral $$E(x)=int_{-infty}^{infty} x p(x,t|x_{0}t_0)$$
So I would like to know how to get aorund this integral? Is there some numerical way to calculate it, or are there even some analytical way to find ?
And of course my complementary error function is defined as:
$$erfc(frac{x+x_{0}-Bt}{2sqrt{Dt}})=frac{2}{sqrt{pi}}int_{frac{x+x_{0}-Bt}{2sqrt{Dt}}}^{infty} e^{-z^2} dz $$
Thanks in advance!
real-analysis integration stochastic-processes stochastic-calculus expected-value
asked Jan 25 at 15:55
George FarahGeorge Farah
65
$endgroup$
add a comment |
$begingroup$
I want to calculate the expected value to the solution of a Fokker-Plank equation, so one of the terms I got includes the complementary error function, namely:
$$p(x,t|x_{0},t_{0})=frac{B}{2 D}*e^{frac{-Bx}{D}} * erfc(frac{x+x_{0}-Bt}{2sqrt{Dt}})$$
So my question is, while calculating the intergral $$E(x)=int_{-infty}^{infty} x p(x,t|x_{0}t_0)$$
So I would like to know how to get aorund this integral? Is there some numerical way to calculate it, or are there even some analytical way to find ?
And of course my complementary error function is defined as:
$$erfc(frac{x+x_{0}-Bt}{2sqrt{Dt}})=frac{2}{sqrt{pi}}int_{frac{x+x_{0}-Bt}{2sqrt{Dt}}}^{infty} e^{-z^2} dz $$
Thanks in advance!
real-analysis integration stochastic-processes stochastic-calculus expected-value
asked Jan 25 at 15:55
George FarahGeorge Farah
65
$endgroup$
add a comment |
$begingroup$
I want to calculate the expected value to the solution of a Fokker-Plank equation, so one of the terms I got includes the complementary error function, namely:
$$p(x,t|x_{0},t_{0})=frac{B}{2 D}*e^{frac{-Bx}{D}} * erfc(frac{x+x_{0}-Bt}{2sqrt{Dt}})$$
So my question is, while calculating the intergral $$E(x)=int_{-infty}^{infty} x p(x,t|x_{0}t_0)$$
So I would like to know how to get aorund this integral? Is there some numerical way to calculate it, or are there even some analytical way to find ?
And of course my complementary error function is defined as:
$$erfc(frac{x+x_{0}-Bt}{2sqrt{Dt}})=frac{2}{sqrt{pi}}int_{frac{x+x_{0}-Bt}{2sqrt{Dt}}}^{infty} e^{-z^2} dz $$
Thanks in advance!
real-analysis integration stochastic-processes stochastic-calculus expected-value
asked Jan 25 at 15:55
George FarahGeorge Farah
65
$endgroup$
I want to calculate the expected value to the solution of a Fokker-Plank equation, so one of the terms I got includes the complementary error function, namely:
$$p(x,t|x_{0},t_{0})=frac{B}{2 D}*e^{frac{-Bx}{D}} * erfc(frac{x+x_{0}-Bt}{2sqrt{Dt}})$$
So my question is, while calculating the intergral $$E(x)=int_{-infty}^{infty} x p(x,t|x_{0}t_0)$$
So I would like to know how to get aorund this integral? Is there some numerical way to calculate it, or are there even some analytical way to find ?
And of course my complementary error function is defined as:
$$erfc(frac{x+x_{0}-Bt}{2sqrt{Dt}})=frac{2}{sqrt{pi}}int_{frac{x+x_{0}-Bt}{2sqrt{Dt}}}^{infty} e^{-z^2} dz $$
Thanks in advance!
real-analysis integration stochastic-processes stochastic-calculus expected-value
real-analysis integration stochastic-processes stochastic-calculus expected-value
asked Jan 25 at 15:55
George FarahGeorge Farah
65
asked Jan 25 at 15:55
George FarahGeorge Farah
65
edited Jan 25 at 16:19
George Farah
asked Jan 25 at 15:55
George FarahGeorge Farah
65
asked Jan 25 at 15:55
George FarahGeorge Farah
65
asked Jan 25 at 15:55
George FarahGeorge Farah
65
65
add a comment |
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