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pro vyhledávání: '"Stable-like processes"'
In the present paper, we introduce so-called operator-stable-like processes. Roughly speaking, they behave locally like operator-stable processes, but they need not to be homogenous in space. Having shown existence for this class of processes, we ana
Externí odkaz:
http://arxiv.org/abs/2011.00783
This paper studies homogenization of symmetric non-local Dirichlet forms with $\alpha$-stable-like jumping kernels in one-parameter stationary ergodic environment. Under suitable conditions, we establish homogenization results and identify the limiti
Externí odkaz:
http://arxiv.org/abs/2003.08581
Autor:
Kolokoltsov, Vassili, Troeva, Marianna
Publikováno v:
PROBLEMY ANALIZA-ISSUES OF ANALYSIS 2018, Vol.7, Issue 2, Pages 69 -81
In this paper we study the sensitivity of nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes. By using the method of stochastic characteristics, we transfer these equations to the non-stochastic equat
Externí odkaz:
http://arxiv.org/abs/1808.04103
Autor:
Jin, Peng
Let $d\ge1$. Consider a stable-like operator of variable order \begin{align*} \mathcal{A}f(x) & =\int_{\mathbb{R}^{d} \backslash\{0\}} \left[f(x+h) -f(x) -\mathbf{1}_{\{|h|\le1\}}h \cdot\nabla f(x)\right]\frac{n(x,h)}{|h|^{d+\alpha(x)}} \mathrm{d}h,
Externí odkaz:
http://arxiv.org/abs/1802.01151
Akademický článek
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Autor:
Jin, Peng
Let $d\ge1$ and $0<\alpha<2$. Consider the integro-differential operator \[ \mathcal{L}f(x) =\int_{\mathbb{R}^{d}\backslash\{0\}}\left[f(x+h)-f(x)-\chi_{\alpha}(h)\nabla f(x)\cdot h\right]\frac{n(x,h)}{|h|^{d+\alpha}}\mathrm{d}h+\mathbf{1}_{\alpha>1}
Externí odkaz:
http://arxiv.org/abs/1709.02836
Autor:
V. N. Kolokoltsov, M. S. Troeva
Publikováno v:
Проблемы анализа, Vol 7(25), Iss 2, Pp 69-81 (2018)
In this paper we study the sensitivity of nonlinear stochastic differential equations of McKean–Vlasov type generated by stable-like processes. By using the method of stochastic characteristics, we transfer these equations to non-stochastic equati
Externí odkaz:
https://doaj.org/article/c937e036b7684e58bc210d9d20ce1d2d
Autor:
Seuret, Stéphane, Yang, Xiaochuan
In this article, we investigate the local behaviors of the occupation measure $\mu$ of a class of real-valued Markov processes M, defined via a SDE. This (random) measure describes the time spent in each set A $\subset$ R by the sample paths of M. We
Externí odkaz:
http://arxiv.org/abs/1605.08594
Autor:
Chen, Zhen-Qing, Zhang, Xicheng
In this work we consider the following $\alpha$-stable-like operator (a class of pseudo-differential operator) $$ {\mathscr L} f(x):=\int_{\mathbb R^d}[f(x+\sigma_x y)-f(x)-1_{\alpha\in[1,2)}1_{|y|\leq 1}\sigma_x y\cdot\nabla f(x)]\nu_x(d y), $$ wher
Externí odkaz:
http://arxiv.org/abs/1604.02681
Autor:
Yang, Xiaochuan
We determine the Hausdorff dimension for the range of a class of pure jump Markov processes in $\mathbb{R}^d$, which turns out to be random and depends on the trajectories of these processes. The key argument is carried out through the SDE representa
Externí odkaz:
http://arxiv.org/abs/1509.08759