Asymptotic estimates of multi-dimensional stable densities and their applications

DOI10.1090/S0002-9947-07-04152-9zbMath1124.62063MaRDI QIDQ3425961

Toshiro Watanabe

Publication date: 7 March 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

spectral measurelast exit timestable sensitytransient Levy process

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Inference from stochastic processes and spectral analysis (62M15) Inference from stochastic processes (62M99) Probabilistic potential theory (60J45) Stable stochastic processes (60G52)

Related Items (39)

Regularity theory for general stable operators ⋮ Estimates of heat kernels of non-symmetric Lévy processes ⋮ TRANSITION DENSITIES OF SUBORDINATORS OF POSITIVE ORDER ⋮ \(L^p\) estimates for degenerate non-local Kolmogorov operators ⋮ Heat kernels for time-dependent non-symmetric stable-like operators ⋮ Parametrix construction of the transition probability density of the solution to an SDE driven by \(\alpha\)-stable noise ⋮ Accuracy of discrete approximation for integral functionals of Markov processes ⋮ Positive definite metric spaces ⋮ Upper estimates of transition densities for stable-dominated semigroups ⋮ Small-time sharp bounds for kernels of convolution semigroups ⋮ On multidimensional stable-driven stochastic differential equations with Besov drift ⋮ A minimal contrast estimator for the linear fractional stable motion ⋮ Estimates of densities for Lévy processes with lower intensity of large jumps ⋮ On weak solutions of SDEs with singular time-dependent drift and driven by stable processes ⋮ Weak well-posedness for a class of degenerate Lévy-driven SDEs with Hölder continuous coefficients ⋮ On some operators associated with non-degenerate symmetric \(\alpha \)-stable probability measures ⋮ Covariance representations, \(L^p\)-Poincaré inequalities, Stein's kernels, and high-dimensional CLTs ⋮ Multivariate stable approximation by Stein's method ⋮ Heat kernels for time-dependent non-symmetric mixed Lévy-type operators ⋮ Anisotropic nonlocal diffusion equations with singular forcing ⋮ Density and tails of unimodal convolution semigroups ⋮ Well-posedness of some non-linear stable driven SDEs ⋮ Spatial asymptotics at infinity for heat kernels of integro-differential operators ⋮ Estimates of tempered stable densities ⋮ Transition density estimates for jump Lévy processes ⋮ On limit theory for functionals of stationary increments Lévy driven moving averages ⋮ A formula for hidden regular variation behavior for symmetric stable distributions ⋮ Approximation of stable-dominated semigroups ⋮ Integral representations of one-dimensional projections for multivariate stable densities ⋮ Schauder estimates for drifted fractional operators in the supercritical case ⋮ Heat kernel of anisotropic nonlocal operators ⋮ Fractional Integrals and Extensions of Selfdecomposability ⋮ Regularity of the density of a stable-like driven SDE with Hölder continuous coefficients ⋮ Boundary Harnack inequality for Markov processes with jumps ⋮ Maximum principles for time-fractional Cauchy problems with spatially non-local components ⋮ Global limit theorems on the convergence of multidimensional random walks to stable processes ⋮ Estimates of transition densities and their derivatives for jump Lévy processes ⋮ On tails of symmetric and totally asymmetric alpha-stable distributions ⋮ Heat kernel of supercritical nonlocal operators with unbounded drifts

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