From discrete equation to ode
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I was wondering in how to convert a moving average of the form:
$$x_t=alpha x_{t-1} + (1-alpha)y_t$$
into an ODE. I thought I could do something like:
$$x_t-x_{t-1} = (alpha-1)(x_t-y_t)$$
and then divide by $Delta_t$ to take limits. But this does not seem to help as it results on an unwanted $Delta_t$ on the rhs before taking the limit ($Delta_t rightarrow 0$) to convert the lfh into a derivative.
differential-equations limits
asked Nov 21 at 11:22
Ambesh
1,4131039
add a comment |
up vote
2
down vote
favorite
I was wondering in how to convert a moving average of the form:
$$x_t=alpha x_{t-1} + (1-alpha)y_t$$
into an ODE. I thought I could do something like:
$$x_t-x_{t-1} = (alpha-1)(x_t-y_t)$$
and then divide by $Delta_t$ to take limits. But this does not seem to help as it results on an unwanted $Delta_t$ on the rhs before taking the limit ($Delta_t rightarrow 0$) to convert the lfh into a derivative.
differential-equations limits
asked Nov 21 at 11:22
Ambesh
1,4131039
Put $beta=frac{(alpha-1)}{Delta_t}$
– user121049
Nov 21 at 12:05
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I was wondering in how to convert a moving average of the form:
$$x_t=alpha x_{t-1} + (1-alpha)y_t$$
into an ODE. I thought I could do something like:
$$x_t-x_{t-1} = (alpha-1)(x_t-y_t)$$
and then divide by $Delta_t$ to take limits. But this does not seem to help as it results on an unwanted $Delta_t$ on the rhs before taking the limit ($Delta_t rightarrow 0$) to convert the lfh into a derivative.
differential-equations limits
asked Nov 21 at 11:22
Ambesh
1,4131039
I was wondering in how to convert a moving average of the form:
$$x_t=alpha x_{t-1} + (1-alpha)y_t$$
into an ODE. I thought I could do something like:
$$x_t-x_{t-1} = (alpha-1)(x_t-y_t)$$
and then divide by $Delta_t$ to take limits. But this does not seem to help as it results on an unwanted $Delta_t$ on the rhs before taking the limit ($Delta_t rightarrow 0$) to convert the lfh into a derivative.
differential-equations limits
differential-equations limits
asked Nov 21 at 11:22
Ambesh
1,4131039
asked Nov 21 at 11:22
Ambesh
1,4131039
edited Nov 21 at 11:44
asked Nov 21 at 11:22
Ambesh
1,4131039
asked Nov 21 at 11:22
Ambesh
1,4131039
asked Nov 21 at 11:22
Ambesh
1,4131039
1,4131039
Put $beta=frac{(alpha-1)}{Delta_t}$
– user121049
Nov 21 at 12:05
add a comment |
Put $beta=frac{(alpha-1)}{Delta_t}$
– user121049
Nov 21 at 12:05
Put $beta=frac{(alpha-1)}{Delta_t}$
– user121049
Nov 21 at 12:05
Put $beta=frac{(alpha-1)}{Delta_t}$
– user121049
Nov 21 at 12:05
add a comment |
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Put $beta=frac{(alpha-1)}{Delta_t}$
– user121049
Nov 21 at 12:05