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Solution to SDE vs long-form notation
Posted: April 20th, 2011, 12:30 pm
by srioae
Hi there,sorry if I'm being daft but I've got a question. Say we've got a SDE in differential formI should really write thisNow if the vol is deterministic I can also write this vol as D(t). Let as then I can also write the solution as How is one the solution and one the correct way of writeing things? If I want to compute expectation do I use the 'solution' SDE?Many thanks
Solution to SDE vs long-form notation
Posted: April 20th, 2011, 12:51 pm
by Alan
Think of W(t) as given; then the soln contains X(t) on the lhs only. Sometimes expectations can be derived from either form.
Solution to SDE vs long-form notation
Posted: April 20th, 2011, 1:01 pm
by srioae
OK I see, and then where there is the special case A(t)=0 the two could be similar (thinking say arithmetic Brownian motion).Thanks,
Solution to SDE vs long-form notation
Posted: April 20th, 2011, 8:40 pm
by Alan
Yes, when the sde coefs don't contain the unknown, then there's no dif.