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

du_{e}(*t,x*) = (Du_{e}(*t, x*) + u_{e}(*t, x*))*dt* + e q
(*t*) *dW _{Q}*(t,x), 0£ t£

and

du_{e}(*t,x*) = Du_{e}(*t, x*)dt + e q
(*t*)(*I*-D)^{-½} *dW*(*t*,*x*), 0 £ t £ T

where D =¶

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

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