On exponential moments of two Brownian functionals

✍ Scribed by Wolfgang Stummer

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 215 KB
• Volume: 31
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(96)00035-1

✦ Synopsis

The aim of this paper is to demonstrate by examples the possible "extreme" behaviour of exponential moments of two Brownian functionals. As a consequence, it will follow that the "uniform" Novikov condition

[(J0

)]
36 > 0: supEx exp 6
IIb(Xs)ll2ds 0: sup Ex[exp(fllb(Xs)[12)] <~ (2) s E [0,T ] and vice versa. Both conditions (1) and (2) are known to be sufficient for the existence of a weak solution of the multidimensional stochastic differential equation dXt = b(Xt)dt + dWt, O<<,t<~ T.