Numerical parameter estimates in stochastic equations with fractional Brownian motion. (English) Zbl 1119.65005

Pospíšil, Jan

Agratini, Octavian (ed.) et al., Proceedings of the international conference on numerical analysis and approximation theory, Cluj-Napoca, Romania, July 4–8, 2006. Cluj-Napoca: Casa Cărţii de Ştiinţă (ISBN 973-686-961-X/hbk). 353-364 (2006).

Summary: We study parameter estimates in stochastic evolution equations driven by fractional Brownian motion. From an observation of the solution on some time interval \([0,T]\), consistent drift estimates are given for \(T\to\infty\). We solve the one-dimensional stochastic differential equation using the Euler-Maruyama method that has been modified so that the driving process is considered to be a fractional Brownian motion. A one-dimensional stochastic partial differential equation is then being solved using the modified finite difference method. In both cases we will use the numerical solution as our observation and we will show how to estimate the parameters from one path only.
For the entire collection see [Zbl 1104.65002].

MSC:

65C30	Numerical solutions to stochastic differential and integral equations
60G30	Continuity and singularity of induced measures
60H15	Stochastic partial differential equations (aspects of stochastic analysis)
35R60	PDEs with randomness, stochastic partial differential equations
35R30	Inverse problems for PDEs
65M32	Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
60H35	Computational methods for stochastic equations (aspects of stochastic analysis)
60J35	Transition functions, generators and resolvents

Keywords:

inverse problem; stochastic evolution equations; stochastic differential equation; Euler-Maruyama method; stochastic partial differential equation; finite difference method