TY - JOUR
T1 - Malliavin calculus for stochastic differential equations driven by subordinated Brownian motions
AU - Kusuoka, Seiichiro
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2010/9
Y1 - 2010/9
N2 - Malliavin calculus is applicable to functionals of stable processes by using subordination. We prepare Malliavin calculus for stochastic differential equations driven by Brownian motions with deterministic time change, and the conditions that the existence and the regularity of the densities inherit from those of the densities of conditional probabilities. By using these, we prove regularity properties of the solutions of equations driven by subordinated Brownian motions.[4] a similar problem is considered.this article we consider more general cases. We also consider equations driven by rotation-invariant stable processes. We prove that the ellipticity of the equations implies the existence of the density of the solution, and we also prove that the regularity of the coefficients implies the regularity of the densities in the case when the equations are driven by one rotation-invariant stable process.
AB - Malliavin calculus is applicable to functionals of stable processes by using subordination. We prepare Malliavin calculus for stochastic differential equations driven by Brownian motions with deterministic time change, and the conditions that the existence and the regularity of the densities inherit from those of the densities of conditional probabilities. By using these, we prove regularity properties of the solutions of equations driven by subordinated Brownian motions.[4] a similar problem is considered.this article we consider more general cases. We also consider equations driven by rotation-invariant stable processes. We prove that the ellipticity of the equations implies the existence of the density of the solution, and we also prove that the regularity of the coefficients implies the regularity of the densities in the case when the equations are driven by one rotation-invariant stable process.
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U2 - 10.1215/0023608X-2010-003
DO - 10.1215/0023608X-2010-003
M3 - Article
AN - SCOPUS:79957803737
VL - 50
SP - 491
EP - 520
JO - Journal of Mathematics of Kyoto University
JF - Journal of Mathematics of Kyoto University
SN - 0023-608X
IS - 3
ER -