The Exit Place of Brownian Motion in an Unbounded Domain

The First Exit Time of Brownian Motion from Unbounded Domain

The First Exit Time of a Brownian Motion from an Unbounded Convex Domain1 By

Consider the first exit time τ D of a (d + 1)-dimensional Brownian motion from an unbounded open domain D = {(x, y) ∈ R d+1 : y > f (x), x ∈ R d } starting at (x 0 , f (x 0) + 1) ∈ R d+1 for some x 0 ∈ R d , where the function f (x) on R d is convex and f (x) → ∞ as the Euclidean norm |x| → ∞. Very general estimates for the asymptotics of log P(τ D > t) are given by using Gaussian techniques. I...

the place of iranian public diplomacy in central asia

چکیده: نسبت به کارکرد و ماهیت دیپلماسی عمومی در جهان امروز نظریه های متعددی بیان گردیده و جایگاه آن در کنار نظریه های دیگر در محافل آکادمیک و دانشگاهی بررسی و تحلیل گردیده است. نظر به اهمیت دیپلماسی عمومی و جایگاه آن در سیاست خارجی ایران این نوشتار با تمرکز بر دیپلماسی عمومی در منطقه آسیای مرکزی تهیه و تنظیم شده است. این ضرورت از آنجا ناشی می شود که اولاً مفهوم دیپلماسی عمومی در سیاست خارجی ای...

Expected Signature of Brownian Motion up to the First Exit Time from a Bounded Domain

The signature of a path provides a top down description of the path in terms of its effects as a control [Differential Equations Driven by Rough Paths (2007) Springer]. The signature transforms a path into a group-like element in the tensor algebra and is an essential object in rough path theory. The expected signature of a stochastic process plays a similar role to that played by the character...

Some Properties of the Exit Measure for Super-brownian Motion

We consider the exit measure of super-Brownian motion with a stable branching mechanism of a smooth domain D of R d. We derive lower bounds for the hitting probability of small balls for the exit measure and upper bounds in the critical dimension. This completes the results given by Sheu 20] and generalizes the results of Abraham and Le Gall 2]. We give also the Hausdorr dimension of the exit m...