Potential theory of subordinate killed Brownian motion in a domain

By Renming Song, Zoran Vondraček. 2003

132 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/0ea9f71ca662e745bfb5a246052c07f1b070fa84

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Two-sided eigenvalue estimates for subordinate processes in domains (2005, background): “1 in[32]) that there existsC ∈ (0,1) such that condition (4.”
Monotonicity and nonexistence results for some fractional elliptic problems in the half-space (2013, background): “4] from a PDE point of view and in [44] in terms of stochastic processes.”
Green Function Estimates and Harnack Inequality for Subordinate Brownian Motions (2006, background): “Some potentialYtheoretic aspects of the subordinate killed Brownian motion (using stable subordinators) were studied in [22, 23].”
Fractional Cauchy problems on bounded domains (2008, background): “If we subordinate Brownian motion X by a stable subordinator Dt in the sense of Bochner, then the conclusions of Corollary 3.2 do not hold since a stable subordinator does not have continuous sample paths; see, for example, Song and Vondrac̆ek [34].”
Distributed-order fractional diffusions on bounded domains (2009, methodology): “ a nondecreasing stable L´evy process Wt, then the conclusions of Corollary 4.2 do not hold, since the stable subordinator does not have continuous sample paths; see, for example, Song and Vondra˘cek [46]. In our case, killing the process B(t) and then applying the time change Et is the same as appl”
A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains (2013, background): “The difference between the two versions of a fractional Laplacian operator on a bounded domain that we are proposing is well-documented in the probabilistic literature [43].”
Potential Theory of Special Subordinators and Subordinate Killed Stable Processes (2006, background): “In [23] and [22], the process Z α was studied in detail and sharp upper and lower bounds on the jumping function and the Green function of Z α were established when D is a bounded C(1,1) domain.”
Trace estimates for stable processes (2007, methodology): “2) We refer the reader to the papers [24] and [13] for many of the basic probabilistic and analytic properties of the processes X̃D t and its transition probabilities.”
Potential theory of subordinate Brownian motions revisited (2011, background): “A fourth notable omission is the potential theory of subordinate killed Brownian motions developed in [21, 22, 37, 38, 40, 41].”
What is the fractional Laplacian? A comparative review with new results (2018, methodology): “The spectral fractional Laplacian with Dirichlet boundary conditions is the generator of subordinate stopped Brownian motion [20], i.”