Determination Properties Research Articles

Moment Determinacy of Powers and Products of Nonnegative Random Variables

We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on conditions about the distribution itself. For the class of generalized gamma random variables, we show that the power and the product of such variables share the same moment determinacy property. A similar statement holds for half-logistic random variables. Besides answering new questions in this area, we either extend some previously known results or provide new and transparent proofs of existing results.

Hamburger moment problem for powers and products of random variables

We present new results on the Hamburger moment problem for probability distributions and apply them to characterize the moment determinacy of powers and products of i.i.d. random variables with values in the whole real line. Detailed proofs of all results are given followed by comments and examples. We also provide new and more transparent proofs of a few known results. E.g., we give a new and short proof that the product of three or more i.i.d. normal random variables is moment-indeterminate. The illustrations involve specific distributions such as the double generalized gamma (DGG), normal, Laplace and logistic. We show that sometimes, but not always, the power and the product of i.i.d. random variables (of the same odd ‘order’) share the same moment determinacy property. This is true for the DGG and the logistic distributions.The paper also treats two unconventional types of problems: products of independent random variables of different types and a random power of a given random variable. In particular, we show that the product of Laplace and logistic random variables, the product of logistic and exponential random variables, the product of normal and χ2 random variables, and the random power ZN, where Z~N and N is a Poisson random variable, are all moment-indeterminate.

A Time Series Analysis of Economical Phenomena in Japan’s Lost Decade (1): Determinacy Property of the Velocity of Money and Equilibrium Solution

The extended velocities of money given by the ratio of NGDP and M2+CD in Japan’s lost decade are analyzed through the non-linear time series analysis based upon the theory of KM2O-Langevin equations. The time series of logarithmic returns of some extended velocities of money are judged to have a determinacy property in a specified time domain whose final time coincides with the time 1999q1 when the Bank of Japan took the zero interest rate policy. This implies that there exists a stochastic process with the time series stated above its realization and it satisfies certain functional relation. This gives a meaning from a viewpoint of time series analysis that the velocity of money can be regarded as an equilibrium solution of the demand and the supply between the goods market and the money market.

Process languages with discrete relative time based on the Ordered SOS format and rooted eager bisimulation

We propose a uniform framework, based on the Ordered Structural Operational Semantics (OSOS) approach of Ulidowski and Phillips [Information and Computation 178 (1) (2002) 180], for process languages with discrete relative time. Our framework allows the user to select favourite process operators, whether they are standard operators or new application-specific operators, provided that they are OSOS definable and their OSOS rules satisfy several simple conditions. The obtained timed process languages preserve a timed version of rooted eager bisimulation preorder and the time determinacy property. We also propose several additional conditions on the type of OSOS definitions for the operators so that several other properties which reflect the nature of time passage, such as the maximal progress, patience and time persistence properties, are also satisfied.

Determinacy of Equilibrium in an Overlapping Generations Model with Heterogeneous Agents

We study the determinacy of perfect foresight equilibrium near a steady state in an overlapping generations model with production and both altruistic and non-altruistic agents having distinct utility functions. The proportion of each type of consumer is exogenously given. Our main results show that when there are positive stationary bequests, some standard assumptions on preferences and technology rule out local indeterminacy for any positive value of the proportions. In the particular case of a separable utility function for altruistic agents, we prove that the determinacy property does not depend on the size of the “infinite lived” altruistic dynasties. Journal of Economic Literature Classification Numbers: C62, D91, O21, O41.

Progress measures, immediate determinacy, and a subset construction for tree automata

Using the concept of progress measure, we give a new proof of Rabin's fundamental result that the languages defined by tree automata are closed under complementation. To do this we show that for certain infinite games based on tree automata, an immediate determinacy property holds for the player who is trying to win according to a Rabin acceptance condition. Immediate determinancy is stronger than the forgetful determinacy of Gurevich and Harrington, which depends on more information about the past, but applies to another class of games. Next, we show a graph theoretic duality theorem for winning conditions. Finally, we present an extended version of Safra's determinization construction. Together, these ingredients and the determinacy of Borel games yield a straightforward recipe for complementing tree automata. Our construction is almost optimal, i.e. the state space blow-up is essentially exponential- thus roughly the same as for automata on finite or infinite words. To our knowledge, no prior constructions have been better than double exponential.

Determinacy of generalized schema

R.M. Karp and R.E. Miller's (1966) computation graphs have been widely studied because they are a useful abstraction of multiprocessor computation. A system has the determinacy property if whenever the same set of input streams are entered into the system, the resultant output is the same set of output streams. Karp and Miller showed that computation graphs have this property; N.S. Woo et al. (1984) showed that dataflow schema also have the property of determinacy. A more general model than either of the foregoing, called a multiple component system model (MCSM), is presently defined. It is proved that MCSMs have the determinacy property. Deadlocking is then defined, and some additional properties of deadlocking MCSMs are proved. >

A proof of the determinacy property of the data flow schema

Previous proofs of data flow determinacy proceeded indirectly and relied on results from abstract semantics. In this paper, a direct proof of the determinacy of data flow schema is given. This proof does not use high powered metamathematical theorems and consequently is accessible to all researchers in data flow, not just those intimately familiar with deep semantic results. Our proof proceeds in three stages. First, the data flow schema which contains instances of Link, Sink and Operator actors is proved to be determinate by reduction to the results of Karp and Miller (1966). Second, data flow schema containing Switch actors, in addition to the above actors, are proved to be determinate. Finally, data flow schema which additionally contain Apply actors are proven to be determinate.