دانلود مقاله انگلیسی فیزیک عمومی رایگان
• سال انتشار:

2020

عنوان انگلیسی مقاله:

On some identities in law involving exponential functionals of Brownian motion and Cauchy random variable

ترجمه فارسی عنوان مقاله:

در مورد برخی از هویت های قانونی مربوط به عملکردهای نمایی حرکت براونی و متغیر تصادفی کوشی

منبع:

Sciencedirect - Elsevier - Stochastic Processes and their Applications, Corrected proof: doi:10:1016/j:spa:2020:05:001

نویسنده:

Yuu Hariya1

چکیده انگلیسی:

Let B = {Bt }t≥0 be a one-dimensional standard Brownian motion, to which we associate the exponential additive functional At = ∫ t 0 e2Bs ds, t ≥ 0. Starting from a simple observation of generalized inverse Gaussian distributions with particular sets of parameters, we show, with the help of a result by Matsumoto and Yor (2000), that, for every x ∈ R and for every positive and finite stopping time τ of the process {e−Bt At }t≥0, the following identity in law holds: (eBτ sinh x + β(Aτ ), CeBτ cosh x + βˆ(Aτ ), e−BτAτ ) (d)= ( sinh(x + Bτ ), C cosh(x + Bτ ), e−BτAτ ) , which extends an identity due to Bougerol (1983) in several aspects. Here β = {β(t)}t≥0 and βˆ = {βˆ(t)}t≥0 are one-dimensional standard Brownian motions, C is a standard Cauchy random variable, and B, β, βˆ and C are independent. The derivation of the above identity provides another proof of Bougerol’s identity in law; moreover, a similar reasoning also enables us to obtain another extension for the three-dimensional random variable ( eBτ sinh x + β(Aτ ), eBτ , Aτ ) . By using an argument relevant to the derivation of those results, some invariance formulae for the Cauchy random variable C involving an independent Rademacher random variable, are presented as well.
Keywords: Brownian motion | Exponential functional | Bougerol’s identity | Cauchy random variable | Generalized inverse Gaussian distribution

سطح: متوسط
تعداد صفحات فایل pdf انگلیسی: 39
حجم فایل: 370 کیلوبایت

قیمت: رایگان

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