Sign in
Help
View Cart
Symmetric Stable Processes as Traces of Degenerate Diffusion Processes
Article Data
History
Submitted: 27 February 1968
Published online: 17 July 2006
Publication Data
ISSN (print): 0040-585X
ISSN (online): 1095-7219
CODEN: tprbau
Copyright © Society for Industrial and Applied Mathematics
Permalink: https://doi.org/10.1137/1114012
Cited by
(2021) A convolution formula for the local time of an Itô diffusion reflecting at 0 and a generalized Stroock–Williams equation. Bernoulli 27:3. Crossref
Christian Glusa, Harbir Antil, Marta D'Elia, Bart van Bloemen Waanders, and Chester J. Weiss. (2021) A Fast Solver for the Fractional Helmholtz Equation. SIAM Journal on Scientific Computing 43:2, A1362-A1388. Abstract | PDF (839 KB) | Supplementary Materials
(2021) Extension technique for functions of diffusion operators: a stochastic approach. Electronic Journal of Probability 26:none. Crossref
(2020) On the harmonic extension approach to fractional powers in Banach spaces. Fractional Calculus and Applied Analysis 23:4, 1054-1089. Crossref
(2020) What is the fractional Laplacian? A comparative review with new results. Journal of Computational Physics 404, 109009. Crossref
(2019) Schauder estimates for drifted fractional operators in the supercritical case. Journal of Functional Analysis, 108425. Crossref
(2019) On the construction and convergence of traces of forms. Journal of Functional Analysis. Crossref
(2019) Asymptotics for the Fractional Allen–Cahn Equation and Stationary Nonlocal Minimal Surfaces. Archive for Rational Mechanics and Analysis 231:2, 1129-1216. Crossref
(2018) Extension technique for complete Bernstein functions of the Laplace operator. Journal of Evolution Equations 18:3, 1341-1379. Crossref
2018. Recent Trends in Free Boundary Regularity. Geometry of PDEs and Related Problems, 147-196. Crossref
(2017) NEXT ORDER ASYMPTOTICS AND RENORMALIZED ENERGY FOR RIESZ INTERACTIONS. Journal of the Institute of Mathematics of Jussieu 16:3, 501-569. Crossref
(2017) Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 34:3, 533-570. Crossref
(2017) Higher regularity of the free boundary in the obstacle problem for the fractional Laplacian. Advances in Mathematics 311, 748-795. Crossref
(2017) Ten equivalent definitions of the fractional laplace operator. Fractional Calculus and Applied Analysis 20:1. Crossref
(2016) Sharp trace Hardy–Sobolev inequalities and fractional Hardy–Sobolev inequalities. Journal of Functional Analysis 270:12, 4513-4539. Crossref
(2016) Ground state solutions for fractional Schrödinger equations with critical Sobolev exponent. Communications on Pure and Applied Analysis 15:3, 991-1008. Crossref
(2016) Fractional Gaussian fields: A survey. Probability Surveys 13:none. Crossref
(2015) 1D log gases and the renormalized energy: crystallization at vanishing temperature. Probability Theory and Related Fields 162:3-4, 795-846. Crossref
(2013) On the Mellin transforms of the perpetuity and the remainder variables associated to a subordinator. Bernoulli 19:4. Crossref
(2013) Functional limit theorems for renewal shot noise processes with increasing response functions. Stochastic Processes and their Applications 123:6, 1987-2010. Crossref
(2013) Hitting Times of Bessel Processes. Potential Analysis 38:3, 753-786. Crossref
(2013) Small mass asymptotic for the motion with vanishing friction. Stochastic Processes and their Applications 123:1, 45-75. Crossref
(2010) Hitting Half-spaces by Bessel-Brownian Diffusions. Potential Analysis 33:1, 47-83. Crossref
(2010) Multiplicative functional for reflected Brownian motion via deterministic ODE. Illinois Journal of Mathematics 54:3. Crossref
(2008) Non-Markovian diffusion equations and processes: Analysis and simulations. Physica A: Statistical Mechanics and its Applications 387:21, 5033-5064. Crossref
(2008) Characterizations and simulations of a class of stochastic processes to model anomalous diffusion. Journal of Physics A: Mathematical and Theoretical 41:28, 285003. Crossref
(2001) Applications of the continuous-time ballot theorem to Brownian motion and related processes. Stochastic Processes and their Applications 95:1, 151-176. Crossref
(2000) Two Coalescents Derived from the Ranges of Stable Subordinators. Electronic Journal of Probability 5:none. Crossref
(1998) Random Brownian scaling identities and splicing of Bessel processes. The Annals of Probability 26:4. Crossref
(1997) The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. The Annals of Probability 25:2. Crossref
(1996) Some independence results related to the arc-sine law. Journal of Theoretical Probability 9:2, 447-458. Crossref
1996. Decomposition at the maximum for excursions and bridges of one-dimensional diffusions. Itô’s Stochastic Calculus and Probability Theory, 293-310. Crossref
(1993) Probabilistic solutions of high order partial differential equations. Physics Letters A 180:3, 225-231. Crossref
(1993) Order statistics for jumps of normalised subordinators. Stochastic Processes and their Applications 46:2, 267-281. Crossref
(1992) Size-biased sampling of Poisson point processes and excursions. Probability Theory and Related Fields 92:1, 21-39. Crossref
(1989) Traces of harmonic functions, capacities, and traces of symmetric Markov processes. Journal of Theoretical Probability 2:4, 399-418. Crossref
1989. Une extension multidimensionnelle de la loi de l'arc sinus. Séminaire de Probabilités XXIII, 294-314. Crossref
1989. Etude d'une martingale remarquable. Séminaire de Probabilités XXIII, 88-130. Crossref
(1987) Mouvement brownien, cônes et processus stables. Probability Theory and Related Fields 76:4, 587-627. Crossref
(1980) On the closability of Dirichlet forms. Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete 51:2, 185-200. Crossref
(1973) Bessel diffusions as a one-parameter family of diffusion processes. Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete 27:1, 37-46. Crossref
1973. The local structure of a class of diffusions and related problems. Proceedings of the Second Japan-USSR Symposium on Probability Theory, 124-169. Crossref
Optimal control based on observations on the boundary. Stochastic Differential Systems, 369-377. Crossref
