For every non-negative number , let X(θ ,t) be a Brownian motion Let Tθ be the first time the process drops a specified amount below its maximum to data. We study stochastic integrals of the form Y(s) = ∫[0, s] v(θ) dw(θ) ,s ≥ 0, where W(θ) = x (θ,T) and V(θ) is a nonanticipating random process. It is assumed that W(θ) has independent increments. We derive an exponential bound for (p(y(s ≥ b))).
El-Nadi, K. (1979). On Some Stochastic Integrals and Dold a Stopped Brownian Motion. The Egyptian Statistical Journal, 23(1), 1-12. doi: 10.21608/esju.1979.315618
MLA
Khairia El-Said El-Nadi. "On Some Stochastic Integrals and Dold a Stopped Brownian Motion", The Egyptian Statistical Journal, 23, 1, 1979, 1-12. doi: 10.21608/esju.1979.315618
HARVARD
El-Nadi, K. (1979). 'On Some Stochastic Integrals and Dold a Stopped Brownian Motion', The Egyptian Statistical Journal, 23(1), pp. 1-12. doi: 10.21608/esju.1979.315618
VANCOUVER
El-Nadi, K. On Some Stochastic Integrals and Dold a Stopped Brownian Motion. The Egyptian Statistical Journal, 1979; 23(1): 1-12. doi: 10.21608/esju.1979.315618
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