ترغب بنشر مسار تعليمي؟ اضغط هنا

A Few Surprising Integrals

157   0   0.0 ( 0 )
 نشر من قبل Malin Pal\\\"o Forsstr\\\"om
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Using formulas for certain quantities involving stable vectors, due to I. Molchanov, and in some cases utilizing the so-called divide and color model, we prove that certain families of integrals which, ostensibly, depend on a parameter are in fact independent of this parameter.



قيم البحث

اقرأ أيضاً

In this article, we develop a framework to study the large deviation principle for matrix models and their quantiz
The theory of one-dimensional stochastic differential equations driven by Brownian motion is classical and has been largely understood for several decades. For stochastic differential equations with jumps the picture is still incomplete, and even som e of the most basic questions are only partially understood. In the present article we study existence and uniqueness of weak solutions to [ {rm d}Z_t=sigma(Z_{t-}){rm d} X_t ]driven by a (symmetric) $alpha$-stable Levy process, in the spirit of the classical Engelbert-Schmidt time-change approach. Extending and completing results of Zanzotto we derive a complete characterisation for existence und uniqueness of weak solutions for $alphain(0,1)$. Our approach is not based on classical stochastic calculus arguments but on the general theory of Markov processes. We proof integral tests for finiteness of path integrals under minimal assumptions.
103 - Mikhail A. Langovoy 2011
We propose an algebraic method for proving estimates on moments of stochastic integrals. The method uses qualitative properties of roots of algebraic polynomials from certain general classes. As an application, we give a new proof of a variation of t he Burkholder-Davis-Gundy inequality for the case of stochastic integrals with respect to real locally square integrable martingales. Further possible applications and extensions of the method are outlined.
Rough paths techniques give the ability to define solutions of stochastic differential equations driven by signals $X$ which are not semimartingales and whose $p$-variation is finite only for large values of $p$. In this context, rough integrals are usually Riemann-Stieltjes integrals with correction terms that are sometimes seen as unnatural. As opposed to those somewhat artificial correction terms, our endeavor in this note is to produce a trapezoid rule for rough integrals driven by general $d$-dimensional Gaussian processes. Namely we shall approximate a generic rough integral $int y , dX$ by Riemann sums avoiding the usual higher order correction terms, making the expression easier to work with and more natural. Our approximations apply to all controlled processes $y$ and to a wide range of Gaussian processes $X$ including fractional Brownian motion with a Hurst parameter $H>1/4$. As a corollary of the trapezoid rule, we also consider the convergence of a midpoint rule for integrals of the form $int f(X) dX$.
292 - Jian Song , Samy Tindel 2021
Given a continuous Gaussian process $x$ which gives rise to a $p$-geometric rough path for $pin (2,3)$, and a general continuous process $y$ controlled by $x$, under proper conditions we establish the relationship between the Skorohod integral $int_0 ^t y_s {mathrm{d}}^diamond x_s$ and the Stratonovich integral $int_0^t y_s {mathrm{d}} {mathbf x}_s$. Our strategy is to employ the tools from rough paths theory and Malliavin calculus to analyze discrete sums of the integrals.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا