TY - JOUR
T1 - Beneš condition for a discontinuous exponential martingale
AU - Liptser, R.
PY - 2013/2
Y1 - 2013/2
N2 - It is known that the Girsanov exponent zt, which is a solution of the Doléans-Dade equation, generated by a Brownian motion Bt and a random process α(t) with, is a martingale provided that the Beneš condition, holds. In this paper, we show that, can lie replaced by a purely discontinuous square integrable martingale Mt with paths from the Skorokhod space D[0,∞) hailing jumps α(s)ΔMt > -1. The method of proof differs from the original Beneš proof. Bibliography: 13 titles.
AB - It is known that the Girsanov exponent zt, which is a solution of the Doléans-Dade equation, generated by a Brownian motion Bt and a random process α(t) with, is a martingale provided that the Beneš condition, holds. In this paper, we show that, can lie replaced by a purely discontinuous square integrable martingale Mt with paths from the Skorokhod space D[0,∞) hailing jumps α(s)ΔMt > -1. The method of proof differs from the original Beneš proof. Bibliography: 13 titles.
UR - http://www.scopus.com/inward/record.url?scp=84880576898&partnerID=8YFLogxK
U2 - 10.1007/s10958-013-1162-7
DO - 10.1007/s10958-013-1162-7
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AN - SCOPUS:84880576898
SN - 1072-3374
VL - 188
SP - 717
EP - 723
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
IS - 6
ER -