Logician Gallery Apprciation

[WhistleBritchesII]

lol

 

[juiceddreadlocks]

listen fuckbor... I'm ugly enough I dont mind having my face beat in to prove a point.

 

[puddlemonkey]

I'm ugly enough I dont mind having my face beat in to prove a point.

co-signed

 

[hurricane]

i dont even know who logician is ? he must be part of the ef secret service

 

[WhistleBritchesII]

loo at fukbor

lol and co-signed

and jus' at Hurricane post stalkcing me

 

[JR76]

= I appreciate him.

 

[samoth]

= I appreciate him.

What's d[Xi,Xj]_s notation in the second term? Designates a set you integrate over? Summation convention?

 

[WhistleBritchesII]

= I appreciate him.

Samoth Just climaxed

 

[JR76]

Here you go Samoth. It's an application of Ito's Lemma, which is one of the fundamental assumptions of advanced financial derivatives, which relies heavily on stochastic calculus, and financial engineering.

Non-continuous semimartingales

Itō's lemma can also be applied to general d-dimensional semimartingales, which need not be continuous. In general, a semimartingale is a cadlag process, and an additional term needs to be added to the formula to ensure that the jumps of the process are correctly given by Itō's lemma. For any cadlag process Yt, the left limit in t is denoted by Yt-, which is a left-continuous process. The jumps are written as ΔYt = Yt - Yt-. Then, Itō's lemma states that if X = (X1,X2,…,Xd) is a d-dimensional semimartingale and f is a twice continuously differentiable real valued function on Rd then f(X) is a semimartingale, and

This differs from the formula for continuous semimartingales by the additional term summing over the jumps of X, which ensures that the jump of the right hand side at time t is Δf(Xt).