As the name indicates, a renewal process is one that “renews” itself regularly. That is, there is a sequence of times {Tn, n ∈ Z} such that the process after time Tn is independent of what happened before that time and has a distribution that does not depend on n. We have seen examples of such processes before. As a simple example, one could consider a Poisson process with jump times Tn. As ano...

Rasmussen develops a new answer to the question, "Why does anything exist?" He begins by describing puzzle about how can exist. The motivates quest explain things as far one can. To solve puzzle, describes sequence of scenes in story existence. brings light three-pronged explanation existence: (i) exist because it is impossible for nothing have existed, (ii) existed there foundational reality t...

A bstract We expand on our results in [1] to present a broad new class of gravitational observables asymptotically Anti-de Sitter space living general codimension-zero regions the bulk spacetime. By taking distinct limits, these can reduce well-studied holographic complexity proposals, e.g., volume maximal slice and action or spacetime Wheeler-DeWitt patch. As with codimension-one family found ...

I propose a new measure of common, time-varying tail risk for large cross sections of stock returns. Stock return tails are described by a power law in which the power law exponent is allowed to transition smoothly through time as a function of recent data. It is motivated by asset pricing theory and is estimable via quasi-maximum likelihood. Estimates indicate substantial time variation in sto...

In a distributed system, it is often important to detect the causal relationships between events, where event e1 is causally before event e2 if e1 happened before e2 and could possibly have aaected the occurrence of e2. In this paper we argue that it can be essential to security that a process determine, in the face of malicious attack, how two events are causally related. We formulate attacks ...

In this article, we present a particle filter (PF)-based track-before-detect (PF TBD) procedure for detection of extended objects whose shape is modeled by an ellipse. By incorporating of an existence variable and the target shape parameters into the state vector, the proposed algorithm performs joint estimation of the target presence/ absence, trajectory and shape parameters under unknown nuis...