<r>In response to 1. It helps if you think about changing the discounting curve as changing the currency. Then the forward rates would have to be different. But in this case the spot FX is always fixed to 1.0. See Bianchetti's paper "two curves one price" <URL url="http://ssrn.com/abstract=1334356">...

Apologies some minor typos:Equation (2.11) and last Equation in page 7: Uppercase "X" in the superscripts should be lowercase "d"

<r>All,I have uploaded the following working note to SSRN. Your comments, suggestions, spotting of typos, missing references are most welcome. <URL url="http://ssrn.com/abstract=2040581Regards">http://ssrn.com/abstract=2040581Regards</URL> MauricioNON-MARTINGALE DYNAMICS FOR TWO CURVE DERIVATIVES PR...

Also if you guys send me your real names (manilla@email.com) I will acknowledge you in my paper for sparing your time in this discussion (if I ever manage to get it published).

<t>QuoteOriginally posted by: Poltermanilla, perhaps you're thinking of something along uniqueness in law, e.g. here (also note the distinction between a strong solution and a weak solution).Yes that is exactly what I am thinking off: Lipschitz and boundedness conditions => Path uniqueness => SDE ha...

<t>QuoteOriginally posted by: list"versions of each other" does not the convenient term because they are defined on different prob. spaces, prob measures P1 and P2 are different. version is used for stoch processes defined on the same prob space with measure P and which coincides for each t with pro...

<t>QuoteOriginally posted by: PolterTake W to be the Wiener process.Let A = W.Let B = -W.Then, A and B have the same distribution at each point in time and dA = dW, while dB = -dW.Is this what you have in mind?I think this example settles the question indeed (I was obviously wrong about the not well...

<t>I think we agree. If the SDE satisfies the usual Lipschitz and boundedness conditions => SDE has uniqueness in Law => process satisfying the SDE with their respective BM's will be versions of each other (I am looking at Lemma 5.3.1 in Oksendal's book). If these conditions are not assumed then equ...

<t>list: OK now you've made me wonder about the generic setting. Suppose I have two stochastic processes over the same state space which are solutions for the same SDE (no restrictions here). If you look at Definition 5.45 in Watkins notes (kindly supplied by Polter above) this does not ensure they ...

<t>list: I agree with what you say, if you want to define the concept accurately it will become very involved. In my modest setting I just needed a generic term to refer to processes with the same law and a simple SDE (with constant or deterministic drift and diffusion coefficients) without having t...

croot: I am writing a paper and would like to thank you in the acknowledgments. If this is OK with you please send your real name to manilla@email.com. Thanks.

<r>It seems the last could correspond to the concept "isonomy class". So far "isonomy" appears to be a bit of an esoteric term as it not in any of the textbooks I have at hand. I've found a definition of isonomy and isonomy class in the following paperCYLINDRICAL MEASURES ON TENSOR PRODUCTS OFBANACH...

Thanks it looks like the correct term. (isonomy = equality in law)

<r>Have a look at Andrew Lesniewski's notes Lecture 4 section 5 Lecture 5 section 6http://<URL url="http://www.math.nyu.edu/~alberts/spring07/index.htmlAlso">www.math.nyu.edu/~alberts/spring07/index.htmlAlso</URL> Vaillant articlehttp://<URL url="http://www.probability.net/convex.pdfPITERBARG-RENEDO...