Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 1, pp. 1--15

NONPARAMETRIC INFERENCE FOR A CLASS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS BASED ON DISCRETE OBSERVATIONS

By

B.L.S. PRAKASA RAO, Indian Statistical Institute, New Delhi

SUMMARY. Consider the stochastic partial differential equations of the type

due(t,x) = (Due(t, x) + ue(t, x))dt + e q (t) dWQ(t,x), 0 t T

and

due(t,x) = Due(t, x)dt + e q (t)(I-D) dW(t,x), 0 t T


where D =2/x2, q Q and Q is a class of positive valued functions such that q2(t) L2(R). We obtain an estimator for the function q(t) based on the Fourier coefficients uie (t), 1 i N of the random field ue(t,x) observed at discrete times and study its asymptotic properties.

AMS (1991) subject classification. Primary 62M40; secondary 60H15.

Key words and phrases. Nonparametric estimation, stochastic partial differential equations, diffusion coefficient, wavelets.

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