Error estimates for a class of finite difference-quadrature schemes for fully nonlinear degenerate parabolic integro-PDEs

被引：12

作者：

Biswas, Imran H. ^{[1
]}

Jakobsen, Espen R. ^{[2
]}

Karlsen, Kenneth H. ^{[1
]}

机构：

[1] Univ Oslo, Ctr Math Applicat, NO-0316 Oslo, Norway

[2] Norwegian Univ Sci & Technol, N-7491 Trondheim, Norway

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2008年 / 5卷 / 01期

关键词：

integro-partial differential equation; viscosity solution; finite difference scheme; error estimate; stochastic optimal control; Levy process; Bellman equation;

D O I：

10.1142/S0219891608001416

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Error estimates are derived for a class of finite difference-quadrature schemes approximating viscosity solutions of nonlinear degenerate parabolic integro-PDEs with variable diffusion coefficients. The relevant equations can be viewed as Bellman equations associated to a class of controlled jump-diffusion (Levy) processes. The results cover both finite and infinite activity cases.

引用

页码：187 / 219

页数：33

共 23 条

[11]

BISWAS IH, 2007, CONT MATH, V429, P19

[12]

Cont R., 2004, FINANCIAL MODELING J

[13] USERS GUIDE TO VISCOSITY SOLUTIONS OF 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS [J].

CRANDALL, MG ;

ISHII, H ;

LIONS, PL .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 27 (01) :1-67

[14]

Fleming W., 2006, CONTROLLED MARKOV PR

[15] Continuous dependence estimates for viscosity solutions of integro-PDEs [J].

Jakobsen, ER ;

Karlsen, KH .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 212 (02) :278-318

[16] On the rate of convergence of approximation schemes for Bellman equations associated with optimal stopping time problems [J].

Jakobsen, ER .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2003, 13 (05) :613-644

[17]

JAKOBSEN ER, UNPUB NUMER MATH

[18] A "maximum principle for semicontinuous functions" applicable to integro-partial differential equations [J].

Jakobsen, Espen R. ;

Karlsen, Kenneth H. .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2006, 13 (02) :137-165

[19] On the rate of convergence of finite-difference approximations for Bellman's equations with variable coefficients [J].

Krylov, NV .

PROBABILITY THEORY AND RELATED FIELDS, 2000, 117 (01) :1-16

[20] The rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients [J].

Krylov, NV .

APPLIED MATHEMATICS AND OPTIMIZATION, 2005, 52 (03) :365-399

← 1 2 3 →