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Entrance laws for coalescing and annihilating Brownian motions

Roger Tribe, Oleg Zaboronski

Abstract

Systems of instantaneously annihilating or coalescing Brownian motions on the line are considered. The extreme points of the set of entrance laws for this process are shown to be Pfaffian point processes at all times and their kernels are identified.

Entrance laws for coalescing and annihilating Brownian motions

Abstract

Systems of instantaneously annihilating or coalescing Brownian motions on the line are considered. The extreme points of the set of entrance laws for this process are shown to be Pfaffian point processes at all times and their kernels are identified.
Paper Structure (2 theorems, 32 equations)

This paper contains 2 theorems, 32 equations.

Key Result

Theorem 1

The extreme elements of the set of entrance laws for $(X_t)$ are $(Q^f: f \in C_{\theta})$ where $C_{\theta} \subseteq L^{\infty}(V_2)$ is given by and for $\theta \in [0,1)$ Moreover these laws $Q^f$ are distinct, that is $f \neq g$ implies $Q^f \neq Q^g$.

Theorems & Definitions (2)

  • Theorem 1
  • Lemma 2