Nizar Demni
We stduy radial Dunkl processes associated with dihedral systems: we derive the semi group, the generalized Bessel function, the Dunkl-Hermite polynomials. Then we give a skew product decomposition by means of independent Bessel processes and we compute the tail distribution of the first hitting time of the boundary of Weyl chamber.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this paper, we establish an integral representation for the density of the reciprocal of the first hitting time of the boundary of even dihedral wedges by a radial Dunkl process having equal multiplicity values. Doing so provides another proof and extends to all even dihedral groups the main result proved in \cite{Demni1}. We also express the weighted Laplace transform of this density through the fourth Lauricella Lauricella function and establish a similar integral representation for odd dihedral wedges.
We give shorter proofs of the following known results: the radial Dunkl process associated with a reduced system and a strictly positive multiplicity function is the unique strong solution for all times of a stochastic differential equation with a singular drift, the first hitting time of the Weyl chamber by a radial Dunkl process is finite almost surely for small values of the multiplicity function. Compared to the original proofs, ours give more information on the behavior of the process. More precisely, the first proof allows to give a positive answer to a conjecture announced by Gallardo a…
Dunkl processes are multidimensional Markov processes defined through the use of Dunkl operators. These processes have discontinuities, and they can be separated into their continuous (radial) part, and their discontinuous (jump) part. While radial Dunkl processes have been studied thoroughly due to their relationship to families of stochastic particle systems such as the Dyson model and Wishart-Laguerre processes, Dunkl jump processes have gone largely unnoticed after the initial work of Gallardo, Yor and Chybiryakov. We study the dynamical properties of these processes, and we derive their m…
Numerical schemes for radial Dunkl processes
该研究针对$\u211d^d$中对应任意既约根系的径向Dunkl过程的数值逼近问题，提出半隐式截断Euler–Maruyama格式，并分析了格式在$L^p$-上确界范数下的收敛速率。
We introduce the analogue of Dunkl processes in the case of an affine root system of type $\widetilde{\text{A}}_1$. The construction of the affine Dunkl process is achieved by a skew-product decomposition by means of its radial part and a jump process on the affine Weyl group, where the radial part of the affine Dunkl process is defined as the unique solution of some stochastic differential equation. We prove that the affine Dunkl process is a càdlàg Markov process as well as a local martingale, study its jumps, and give a martingale decomposition, which are properties similar to those of the …
We provide two equivalent approaches for computing the tail distribution of the first hitting time of the boundary of the Weyl chamber by a radial Dunkl process. The first approach is based on a spectral problem with initial value. The second one expresses the tail distribution by means of the $W$-invariant Dunkl-Hermite polynomials. Illustrative examples are given by the irreducible root systems of types $A$, $B$, $D$. The paper ends with an interest in the case of Brownian motions for which our formulae take determinantal forms.
In this paper, we derive an integral representation for the density of the reciprocal of the first hitting time of the boundary of a wedge of angle $π/4$ by a radial Dunkl process with equal multiplicity values. Not only this representation readily yields the non negativity of the density, but also provides an analogue of Dufresne's result on the distribution of the first hitting time of zero by a Bessel process and a generalization of the Vakeroudis-Yor's identity satisfied by the first exit time from a wedge by a planar Brownian motion. We also use a result due to Spitzer on the angular part…
We work out the expression of the generalized Bessel function of type B in the two-rank case. This is done using Dijskma and Koornwinder's product formula for Jacobi polynomials and the obtained expression is given by multiple integrals involving only a normalized modified Bessel function and two symmetric Beta distributions. We think of that expression as the major step toward the explicit expression of the Dunkl's intertwining V operator reflections-invariant functions. Finally, we give in the same setting an explicit formula for the action of V on a product of a power of the norm and a sphe…
Asymptotics of Generalized Bessel Functions and Weight Multiplicities via Large Deviations of Radial Dunkl Processes
本文基于径向 Dunkl 过程流体力学极限的大偏差原理，证明了广义 Bessel 函数的大 N 渐近变分公式及径向 Heckman-Opdam 过程的大偏差原理，并应用于确定大秩极限下单李代数不可约表示的权重重数渐近行为。
We begin with the study of some properties of the radial Dunkl process associated to a reduced root system $R$. It is shown that this diffusion is the unique strong solution for all $t \geq 0$ of a SDE with singular drift. Then, we study $T_0$, the first hitting time of the positive Weyl chamber : we prove, via stochastic calculus, a result already obtained by Chybiryakov on the finiteness of $T_0$. The second and new part deals with the law of $T_0$ for which we compute the tail distribution, as well as some insight via stochastic calculus on how root systems are connected with eigenvalues of…
In this paper we obtain skew-product representations of the multidimensional Dunkl processes which generalize the skew-product decomposition in dimension 1 obtained in L. Gallardo and M. Yor. Some remarkable properties of the Dunkl martingales. Séminaire de Probabilités XXXIX, 2006. We also study the radial part of the Dunkl process, i.e. the projection of the Dunkl process on a Weyl chamber.
Strong solution and approximation of time-dependent radial Dunkl processes with multiplicative noise
本文研究了一类由乘性噪声驱动的时变粒子系统在Weyl室内的强解存在性与唯一性，提出证明解存在负矩的方法，并据此分析了两种逼近解的数值方案。
Bessel and Dunkl processes with drift
本文研究了带有漂移的贝塞尔和杜克尔过程的构造及其特性，包括径向部分、吉拉斯定理、矩、鞅、大数定律和中心极限定理。
Generalized Bessel-Dunkl diffusions
本文针对经典根系Weyl室中的Bessel-Dunkl型扩散，建立了包含时变、位变系数及可退化奇异排斥项的统一理论，证明了弱存在性、路径唯一性、强存在性及平均场收敛定理。
We introduce and study the natural counterpart of the Dunkl Markov processes in a negatively curved setting. We give a semimartingale decomposition of the radial part, and some properties of the jumps. We prove also a law of large numbers, a central limit theorem, and the convergence of the normalized process to the Dunkl process. Eventually we describe the asymptotic behavior of the infinite loop as it was done by Anker, Bougerol and Jeulin in the symmetric spaces setting in \cite{ABJ}.
The radial probability measures on $R^p$ are in a one-to-one correspondence with probability measures on $[0,\infty[$ by taking images of measures w.r.t. the Euclidean norm mapping. For fixed $ν\in M^1([0,\infty[)$ and each dimension p, we consider i.i.d. $R^p$-valued random variables $X_1^p,X_2^p,...$ with radial laws corresponding to $ν$ as above. We derive weak and strong laws of large numbers as well as a large deviation principle for the Euclidean length processes $S_k^p:=\|X_1^p+...+X_k^p\|$ as k,p\to\infty in suitable ways. In fact, we derive these results in a higher rank setting, wher…
Collision times of multivariate Bessel processes with their Weyl chambers' boundaries and their Hausdorff dimension
本文利用交错多项式平方将 A 型 Dyson 模型碰撞时间的 Hausdorff 维数结果推广至所有有理型多元 Bessel 过程，证明其仅依赖多重性函数最小值且与空间维数、粒子数无关。
Some freezing limits for Bessel functions and Bessel processes with drift of type $B_N$
本文利用 Jack 多项式级数表示，证明了 $B_N$ 型贝塞尔函数及其导数在参数 $k_1\to\infty$ 时的冻结极限，并由此得到带漂移贝塞尔过程的弱极限，应用于矩阵空间上带漂移布朗运动的径向部分。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。