Help

[icedebris]

Hello,

Thank you for writing a code to solve FPE. The examples seem to use some physics language, which I find difficult to translate to "standard" math formulation. Can you please let me know how to setup a problem to solve the following problem. Suppose the two state-variables follow

dy_t = x_tdt
dx_t = f(x_t, y_t)dt + bdW_t,
where b is a constant and f(x_t, y_t) is a general function (it ensures that x_t and y_t have stationary dynamics on 0<x<inf, y<0<inf).

I would like to solve for a stationary density g, which amount to solving the following FPE: -xg'_y - (f(x,y)g)'_x +b^2*g''_xx/2 = 0. Does you code allow to solve this problem? And if so, how one can do that?

Many thanks,
Igor

[JiejunHu]

Hello,

Thank you for writing a code to solve FPE. The examples seem to use some physics language, which I find difficult to translate to "standard" math formulation. Can you please let me know how to setup a problem to solve the following problem. Suppose the two state-variables follow

dy_t = x_tdt dx_t = f(x_t, y_t)dt + bdW_t, where b is a constant and f(x_t, y_t) is a general function (it ensures that x_t and y_t have stationary dynamics on 0<x<inf, y<0<inf).

I would like to solve for a stationary density g, which amount to solving the following FPE: -xg'_y - (f(x,y)g)'_x +b^2*g''_xx/2 = 0. Does you code allow to solve this problem? And if so, how one can do that?

Many thanks, Igor

Dear Igor, is there an answer to your question? Thank you!

[icedebris]

No, I haven't gotten any reply. In the end, I simulated the process in Julia to obtain the density. Best wishes, Igor Sent with [ProtonMail](https://protonmail.com/) Secure Email. ‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐

…

On Tuesday, November 30th, 2021 at 17:47, JiejunHu ***@***.***> wrote: > Hello, > > Thank you for writing a code to solve FPE. The examples seem to use some physics language, which I find difficult to translate to "standard" math formulation. Can you please let me know how to setup a problem to solve the following problem. Suppose the two state-variables follow > > dy_t = x_tdt dx_t = f(x_t, y_t)dt + bdW_t, where b is a constant and f(x_t, y_t) is a general function (it ensures that x_t and y_t have stationary dynamics on 0<x<inf, y<0<inf). > > I would like to solve for a stationary density g, which amount to solving the following FPE: -xg'_y - (f(x,y)g)'_x +b^2*g''_xx/2 = 0. Does you code allow to solve this problem? And if so, how one can do that? > > Many thanks, Igor Dear Igor, is there an answer to your question? Thank you! — You are receiving this because you authored the thread. Reply to this email directly, [view it on GitHub](#4 (comment)), or [unsubscribe](https://github.com/notifications/unsubscribe-auth/ASXWKHCCHO2I6QSF7G2PVYTUOUE2PANCNFSM4XE3FKRQ). Triage notifications on the go with GitHub Mobile for [iOS](https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675) or [Android](https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub).