Time-dependent rate of convergence for binomial approximations

Por • 23 sep, 2016 • Sección: Opinion

Antti Luoto

Abstract: Let W  be a Brownian motion. Then u(t,x)=E[g(x+σW Tt )]  is the solution of the backward heat equation with terminal condition g  . Let v n (t,x)  denote the according approximation produced by a simple random walk. This paper is concerned with the rate of convergence of v n (t,x)  to u(t,x)  for functions g  of bounded variation and Lipschitz functions, and the behavior of the error v n (t,x)−u(t,x)  as t  tends to T  .

arXiv:1609.05768v1 [math.PR]

Probability (math.PR)

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