Abstract
LET X(T) BE A DIFFUSION SATISFYING THE STOCHASTIC DIFFERENTIAL EQUATION DX(T) = F(X(T))DT + DB(T), WHERE F ' (X) = F**2(X) = AX**2 + BX + C, A > 0. V. BENES GAVE AN EXPLICIT FORMULA FOR THE CONDITIONAL DENSITY OF X(T) GIVEN Y(S), 0 < S < T, WHERE Y(S) = ″INTEGRAL″ **T//0X(S)DS + W(T), WHEN W( * ) IS A BROWNIAN PROCESS INDEPENDENT OF X( * ). THE RESULT IS EXTENDED AND THEN APPLIED TO DERIVE RECURSIVE FILTERING EQUATIONS FOR ESTIMATING CONDITIONAL MOMENTS, FOR ESTIMATING POLYNOMIAL FUNCTIONALS OF X( * ), AND FOR SMOOTHING.
Original language | English (US) |
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Pages (from-to) | 1-16 |
Number of pages | 16 |
Journal | STOCHASTICS |
Volume | V 8 |
Issue number | N 1 |
DOIs | |
State | Published - 1982 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modeling and Simulation