On Some Stochastic Integrals and a Stopped Brownian Motion | ||
| The Egyptian Statistical Journal | ||
| Article 1, Volume 23, Issue 1, June 1979, Pages 1-12 PDF (5.41 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.1979.315618 | ||
| Author | ||
| Khairia El-Said El-Nadi | ||
| Alexandria University, Egypt. | ||
| Abstract | ||
| 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))). | ||
| Keywords | ||
| Stochastic Integrals - Dold A Stopped Brownian Motion; Non anticipating Random Process - Exponential Bound | ||
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