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Process Level Large Deviations for a Class of Piecewise Homogeneous Random Walks.- Mutual Singularity of Genealogical Structures of Fleming-Viot and Continuous Branching Processes.- Regular Conditional Expectations and the Continuum Hypothesis.- Necessary and Sufficient Conditions for Weak Convergence of One-Dimensional Markov Processes.- Inverse Subordination of Excessive Functions.- Jumping Branching Measure-Valued Processes.- The Boundedness of Branching Markov Processes.- A Limit Theorem for Weighted Branching Process Trees.- Loop Condensation Effects in the Behavior of Random Walks.- On the Stability of Solutions of Stochastic Evolution Equations.- Harmonic Functions on Riemannian Manifolds: A Probabilistic Approach.- On a Problem Suggested by A.D. Wentzell.- Regularity Properties of a Supercritical Superprocess.- A Lemma on Super-Brownian Motion with Some Applications.- Sequential Screening of Significant Variables of an Additive Model.- Brownian Bandits.- Lyapunov Exponents and Distributions of Magnetic Fields in Dynamo Models.- The Strong Markov Property of the Support of Super-Brownian Motion.- Some Results on Random Walks on Groups.- Diffusions as Integral Curves, or Stratonovich without Itô.- Convex Solutions to Variational Inequalities and Multidimensional Singular Control.- Regularity of Self-Diffusion Coefficient.- Representation Results for Stopping Times in Jump-with-Drift Processes.