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- 2Heavy tails
- 2Large deviations principle
- 2Linear process
- 2Long-range dependence
- 2Marcinkiewicz strong law of large numbers
- 2Stochastic approximation
We address the missing analog of vague convergence in the weak-converge large-deviations analogy. Specifically, we introduce the weak Laplace principle and show it implies both the well-known weak LDP and the Laplace principle lower bound. Both the weak LDP and weak Laplace principle hold in...
The equivalences to and the connections between the modulus-of-continuity condition, compact containment and tightness on DE[a, b] with a < b are studied. The results within are tools for establishing tightness for probability measures on DE[a, b] that generalize and simplify prevailing results...
Partially-observed microstructure models, containing stochastic volatility, dynamic trading noise and short term inertia, are introduced to address the following questions: (1) Do the observed prices exhibit statistically signicant inertia? (2) Is stochastic volatility (SV) still evident in the...
The classical particle filter, introduced in 1993, approximates the normalized filter directly. It has two defiencies, over resampling and the inability to distinguish models, the former of which was overcome but the later is fundamental. Conversely, the weighted particle filter, motivated by the...