Recent content by cernlife

sorry, it was meant to be (1-s/t)_+ that was a typo... although I did enter it correctly into Mathematica... basically what I am looking at is a theorem from the paper "fractional tempered stable motion" and also work from the paper "Integrating volatility clustering into exponential Levy...

I'm struggling to work out how to integrate the following \int_0^t(\gamma^{1/\kappa}-i\zeta{w}(1-t/s)_+^{H-1/2})^{\kappa}ds here (.)_+ denotes the positive part if I did not have the ^(H-1/2) I can do it, alas it does have it! and so it stumps me on how to evaluate this integral. any...

"micromass" thanks again, that sounds promising, so if my kernal was given by K_{\alpha}(t,s)=\frac{1}{ \Gamma(\alpha)A}(t-s)^{\alpha-1} and \phi(s)=\frac{ \Gamma(1-\alpha)}{\alpha}((1/2)\gamma^{1/\alpha})^{\alpha}-((1/2)\gamma^{1/\alpha}-is)^{\alpha} I guess I am trying to evaluate...

"I like Serena", in answer to your second comment In the paper "A new tempered stable distribution and its applications to finance" by Rachev and Kim, they define a tempered stable distribution by tempering a symmetric stable distribution (defined on the whole real line), which is slightly...

Thank you for the further reply 'micromass'. The reason why I need the expression for R(dx) is due to another part of my work which relates to the paper "On fractional tempered stable motion" by C.Houdre and R.Kawai. In this paper they define (definition 2.4) Fractional tempered stable...

Here is the context, its a bit long, so please bear with me... M is the Levy measure of the tempered stable distribution, which we can check as follows We define a stable distribution as (in paramitization) s_{\alpha,\delta} = s(y; \alpha, (\delta{2^{\alpha}}cos(\pi\alpha/2)^{1/\alpha}...

yes very obscure to myself do you have any notion how to get the expression R(dx) = ...dx That I so badly need?

Thanks "I like Serena" for the reply, much appreciated. However I still don't have the slightest clue how to get my R(dx)=...some kind of equation... when I say "some kind of equation" I mean like R(dx) = (2^{\alpha}\delta\frac{\alpha}{ \Gamma(1-\alpha)})dx or something like that...

are you sure? In theorem 2.3 (as written above) they say M(A) = \int_{R^d} \int_0^{\infty} I_A(tx)t^{-\alpha-1}e^{-t}dtR(dx) now I know the levy measure M in my case, i.e when the tempering function is e^{-(1/2)\gamma^{1/\alpha}x} is M(dx) = 2^{\alpha}\delta\frac{\alpha}{...

Yes R is just a measure. Yes you make perfect sense, by that I mean in the paper I am talking about they also write "This yields a change of variable formula" \int_{R^d} R(dx) = \int_{R^d} F(x/||x||^2)R(dx) between equations (2.5) and (2.6). However, I am still as lost as every as...

My question is how to compute R(dx). But before I can ask that I have to write down the background to my problem, so bear withme ---------------------------------------------------------------------------- A tempered stable distribution is when a stable distribution is tempered by an...

I am trying to find a function R(dx) in a paper by Rosinski "Tempering Stable Processes" which has the following theorem Theorem 2.3. The Levy measure M of a tempered alpha stable distribution can be written in the form M(A) = \int_{R^d}\int_0^{\infty}...

I'm reading this journal article and they keep on using the notation \int_{R^d} What does this mean, just say d=1, does it then mean \int_0^{\infty} or \int_{-\infty}^{\infty} any help much appreciated.