Rate of Convergence of the Euler Approximation for Diffusion Processes

1991 ◽  
Vol 151 (1) ◽  
pp. 233-239 ◽  
Author(s):  
Remigius Mikulevicius ◽  
Eckhard Plate
Keyword(s):  
Rate Of Convergence ◽  
Diffusion Processes ◽  
Euler Approximation

scholarly journals ON APPROXIMATION OF VALUE FUNCTIONS FOR CONTROLLED DISCONTINUOUS RANDOM PROCESSES

2011 ◽  
Vol 16 (1) ◽  
pp. 260-272
Author(s):  
Svetlana Danilenko ◽  
Henrikas Pragarauskas
Keyword(s):  
Rate Of Convergence ◽  
General Class ◽  
Diffusion Processes ◽  
Random Processes ◽  
Value Functions ◽  
Control Policies ◽  
Controlled Processes ◽  
Constant Control

We consider the problem of approximation of value functions for controlled possibly degenerated diffusion processes with jumps by using piece-wise constant control policies. A rate of convergence for the corresponding value functions is established provided that the coefficients of controlled processes are sufficiently smooth. The paper extends the results of N.V. Krylov to a more general class of controlled processes.

scholarly journals Edgeworth expansion for Euler approximation of continuous diffusion processes

2020 ◽  
Vol 30 (4) ◽  
pp. 1971-2003
Author(s):  
Mark Podolskij ◽  
Bezirgen Veliyev ◽  
Nakahiro Yoshida
Keyword(s):  
Edgeworth Expansion ◽  
Diffusion Processes ◽  
Euler Approximation

A symmetrized Euler scheme for an efficient approximation of reflected diffusions

2004 ◽  
Vol 41 (03) ◽  
pp. 877-889 ◽  
Author(s):  
Mireille Bossy ◽  
Emmanuel Gobet ◽  
Denis Talay
Keyword(s):  
Rate Of Convergence ◽  
Diffusion Processes ◽  
Smooth Boundary ◽  
Time Discretization ◽  
Euler Scheme ◽  
Oblique Reflection ◽  
Reflected Diffusions ◽  
Discretization Step ◽  
Efficient Approximation

In this article, we analyse the error induced by the Euler scheme combined with a symmetry procedure near the boundary for the simulation of diffusion processes with an oblique reflection on a smooth boundary. This procedure is easy to implement and, in addition, accurate: indeed, we prove that it yields a weak rate of convergence of order 1 with respect to the time-discretization step.

A symmetrized Euler scheme for an efficient approximation of reflected diffusions

2004 ◽  
Vol 41 (3) ◽  
pp. 877-889 ◽  
Author(s):  
Mireille Bossy ◽  
Emmanuel Gobet ◽  
Denis Talay
Keyword(s):  
Rate Of Convergence ◽  
Diffusion Processes ◽  
Smooth Boundary ◽  
Time Discretization ◽  
Euler Scheme ◽  
Oblique Reflection ◽  
Reflected Diffusions ◽  
Discretization Step ◽  
Efficient Approximation

In this article, we analyse the error induced by the Euler scheme combined with a symmetry procedure near the boundary for the simulation of diffusion processes with an oblique reflection on a smooth boundary. This procedure is easy to implement and, in addition, accurate: indeed, we prove that it yields a weak rate of convergence of order 1 with respect to the time-discretization step.

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