A decomposition theorem for supermartingales

Decomposition of Supermartingales Indexed by a Linearly Ordered Set

We prove a version of the Doob Meyer decomposition for supermartingales with a linearly ordered index set. Key words Doob Meyer decomposition, natural increasing processes, potentials, supermartingales. Mathematics Subject Classi…cation (2000): : 28A12, 60G07, 60G20.

A Decomposition Theorem for Domains

A domain constructor that generalizes the product is de ned. It is shown that with this constructor exactly the prime-algebraic coherent Scott-domains and the empty set can be generated from two-chains and boolean at domains. 3 List of Symbols I am identifying the symbols by the corresponding Latex(+Amssymb)-symbols. " uparrow # downarrow ! rightarrow ? bot > top leq geq 2 in W bigvee V bigwedg...

A maximal inequality for supermartingales∗

A tight upper bound is given on the distribution of the maximum of a supermartingale. Specifically, it is shown that if Y is a semimartingale with initial value zero and quadratic variation process [Y, Y ] such that Y + [Y, Y ] is a supermartingale, then the probability the maximum of Y is greater than or equal to a positive constant a is less than or equal to 1/(1 + a). The proof makes use of ...

A Martingale Decomposition Theorem

A Cohomology Decomposition Theorem

In [9] Jackowski and McClure gave a homotopy decomposition theorem for the classifying space of a compact Lie group G; their theorem states that for any prime p the space BG can be constructed at p as the homotopy direct limit of a specific diagram involving the classifying spaces of centralizers of elementary abelian p-subgroups of G. In this paper we will prove a parallel algebraic decomposit...