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Brownian Mechanics
I was wondering if it is possible to model brownian motion with drift mathematicallythe way newtonian mechanics does it
Brownian Mechanics
... hmm..., not exactly sure what you mean here...If you are referring to using standard "Newtonian" calculus, the answer is most definitely no, as GBM is continuous everywhere but differentiable nowhere in the normal sense, thus the standard chain rule for differentiation doesn't apply. Hence the need for Ito calculus.Other than that, I'm not sure as to what connection you seek with GBM and Newtonian mechanics.
Last edited by spongebob on February 24th, 2004, 11:00 pm, edited 1 time in total.
Brownian Mechanics
wasn't thinking abt differentiation or integrationsince most of the random processes in finance are modelled by brownian motionso what happens when a brownian motion experiences some external force ( in newtonian mechanics it is f=ma)now this force we can translate it to an event say 9/11 in finance termand it will provide some acceleration towards some perceived destination for a whilewhile there might be some resistance for at the moment.yup I am trying to formulate it
Brownian Mechanics
Have you had a look at Merton's Jump-Diffusion model?
Brownian Mechanics
This is classical heat conduction problem - conduction of heat through a semi-infinite slab with a heated surface. Solutions abound in any undergrad heat transfer text.
Brownian Mechanics
Check out also the Rayleigh problem in any undergrad/grad fluid mechanics text. It describes the viscosity-driven flow due to the sudden start of an infinite flat plate.
Last edited by rcohen on February 26th, 2004, 11:00 pm, edited 1 time in total.
Brownian Mechanics
-- A Scott Caveny type deletion --
Last edited by N on February 29th, 2004, 11:00 pm, edited 1 time in total.