摘要:

There is a lack of appropriate replication of the asymptotical behaviour of stationary stochastic differential equations solved by numerical methods. The paper illustrates this fact with the stationary Ornstein-Uhlenbeck process and family of implicit Euler methods. For description of occuring bias, notions of asymptoticalp-th. mean, mean, mean square and equilibrium preservation are introduced, due to stochasticity of stationary law. Only the trapezoidal formula among these methods is optimal in the sense of replication of exact asymptotical behaviour. We also discuss the general probabilistic law of linear Euler methods. The results can be useful for implementation of stochastic-numerical algorithms (e.g. for linear-implicit methods) in several disciplines of Natural and Environmental Sciences

ISSN:0736-2994    

DOI:10.1080/07362999908809613

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

Elliptic equations in infinitely many variables are here studied by a semigroup vapproach. Using interpolation theory Schauder estimates for the solutions to such equations are derived. As a consequence, a uniqueness in law result for the correspondig infinite-dimensional stochastic differential equation is obtained

ISSN:0736-2994    

DOI:10.1080/07362999908809614

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0736-2994    

DOI:10.1080/07362999908809602

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor