Time-dependent weak rate of convergence for functions of generalized bounded variation
Finna-arvio
Time-dependent weak rate of convergence for functions of generalized bounded variation
Time%20dependent%20weak%20rate%20of%20convergence%20for%20functions%20of%20generalized%20bounded%20variation.pdf
(Jyväskylän yliopisto - JYX)
Let W denote the Brownian motion. For any exponentially bounded Borel function g the function u defined by u(t,x)=E[g(x+σWT−t)] is the stochastic solution of the backward heat equation with terminal condition g. Let un(t,x) denote the corresponding approximation generated by a simple symmetric random walk with time steps 2T/n and space steps ±σ√T/n where σ>0. For a class of terminal functions g having bounded variation on compact intervals, the rate of convergence of un(t,x) to u(t, x) is considered, and also the behavior of the error un(t,x)−u(t,x) as t tends to T.
Tallennettuna:
Kieli |
englanti |
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Sarja | Stochastic Analysis and Applications, 3 |
Aiheet | |
ISSN |
0736-2994 |