Why can the stochastic integral $int_t_i^t_i+1 sigma(t,X(t))dW(t) $ approximated by $sigma(t_i,X(t_i))(W(t_i+1)-W(t_i))$? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Compute a stochastic integralApproximation of Stochastic integral with Stieltjes integrals“Continuity” of stochastic integral wrt Brownian motionCalculate Stochastic IntegralBrownian Motion and stochastic integration on the complete real lineThe independence between stochastic integral and sigma-algebraThe limit of the ratio of two stochastic integralsthe exact integrand space for stochastic integral?Comparison of variance of stochastic and non-stochastic integrals of the Brownian motionfiltration of a stochastic integral
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Why can the stochastic integral $int_t_i^t_i+1 sigma(t,X(t))dW(t) $ approximated by $sigma(t_i,X(t_i))(W(t_i+1)-W(t_i))$?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Compute a stochastic integralApproximation of Stochastic integral with Stieltjes integrals“Continuity” of stochastic integral wrt Brownian motionCalculate Stochastic IntegralBrownian Motion and stochastic integration on the complete real lineThe independence between stochastic integral and sigma-algebraThe limit of the ratio of two stochastic integralsthe exact integrand space for stochastic integral?Comparison of variance of stochastic and non-stochastic integrals of the Brownian motionfiltration of a stochastic integral
$begingroup$
Why can the stochastic integral $int_t_i^t_i+1 sigma(t,X(t))dW(t) $ be approximated by $sigma(t_i,X(t_i))(W(t_i+1)-W(t_i))$ in the Euler scheme? Here $sigma$ can be thought of as a lipschitz continuous bounded function and $W$ as the standard one-dimensional Brownian motion
If this were a path by path integral($omega$-wise in the Lebesgue Stieltges sense) , I would have no apprehensions what so ever. But the stochastic integral isnt defined path-wise. Does is have to do with the way we define stochastic integrals of simple functions with respect to the Brownian motion?
numerical-methods stochastic-integrals
asked Mar 27 at 15:37
user3503589user3503589
1,3351921
$endgroup$
add a comment |
$begingroup$
Why can the stochastic integral $int_t_i^t_i+1 sigma(t,X(t))dW(t) $ be approximated by $sigma(t_i,X(t_i))(W(t_i+1)-W(t_i))$ in the Euler scheme? Here $sigma$ can be thought of as a lipschitz continuous bounded function and $W$ as the standard one-dimensional Brownian motion
If this were a path by path integral($omega$-wise in the Lebesgue Stieltges sense) , I would have no apprehensions what so ever. But the stochastic integral isnt defined path-wise. Does is have to do with the way we define stochastic integrals of simple functions with respect to the Brownian motion?
numerical-methods stochastic-integrals
asked Mar 27 at 15:37
user3503589user3503589
1,3351921
$endgroup$
add a comment |
$begingroup$
Why can the stochastic integral $int_t_i^t_i+1 sigma(t,X(t))dW(t) $ be approximated by $sigma(t_i,X(t_i))(W(t_i+1)-W(t_i))$ in the Euler scheme? Here $sigma$ can be thought of as a lipschitz continuous bounded function and $W$ as the standard one-dimensional Brownian motion
If this were a path by path integral($omega$-wise in the Lebesgue Stieltges sense) , I would have no apprehensions what so ever. But the stochastic integral isnt defined path-wise. Does is have to do with the way we define stochastic integrals of simple functions with respect to the Brownian motion?
numerical-methods stochastic-integrals
asked Mar 27 at 15:37
user3503589user3503589
1,3351921
$endgroup$
Why can the stochastic integral $int_t_i^t_i+1 sigma(t,X(t))dW(t) $ be approximated by $sigma(t_i,X(t_i))(W(t_i+1)-W(t_i))$ in the Euler scheme? Here $sigma$ can be thought of as a lipschitz continuous bounded function and $W$ as the standard one-dimensional Brownian motion
If this were a path by path integral($omega$-wise in the Lebesgue Stieltges sense) , I would have no apprehensions what so ever. But the stochastic integral isnt defined path-wise. Does is have to do with the way we define stochastic integrals of simple functions with respect to the Brownian motion?
numerical-methods stochastic-integrals
numerical-methods stochastic-integrals
asked Mar 27 at 15:37
user3503589user3503589
1,3351921
asked Mar 27 at 15:37
user3503589user3503589
1,3351921
asked Mar 27 at 15:37
user3503589user3503589
1,3351921
asked Mar 27 at 15:37
user3503589user3503589
1,3351921
asked Mar 27 at 15:37
user3503589user3503589
1,3351921
1,3351921
add a comment |
add a comment |
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