Simple Recursion

2016 ◽  
pp. 45-59
Keyword(s):  
Simple Recursion

scholarly journals A multivariate regime-switching GARCH model with an application to global stock market and real estate equity returns

2018 ◽  
Vol 22 (3) ◽  
Author(s):  
Markus Haas ◽  
Ji-Chun Liu
Keyword(s):  
Real Estate ◽  
Stock Market ◽  
Regime Switching ◽  
Markov Switching ◽  
Garch Model ◽  
Equity Returns ◽  
Out Of Sample ◽  
High Volatility ◽  
Simple Recursion ◽  
Global Stock

AbstractWe consider a multivariate Markov-switching GARCH model which allows for regime-specific volatility dynamics, leverage effects, and correlation structures. Conditions for stationarity and expressions for the moments of the process are derived. A Lagrange Multiplier test against misspecification of the within-regime correlation dynamics is proposed, and a simple recursion for multi-step-ahead conditional covariance matrices is deduced. We use this methodology to model the dynamics of the joint distribution of global stock market and real estate equity returns. The empirical analysis highlights the importance of the conditional distribution in Markov-switching time series models. Specifications with Student’stinnovations dominate their Gaussian counterparts both in- and out-of-sample. The dominating specification appears to be a two-regime Student’stprocess with correlations which are higher in the turbulent (high-volatility) regime.

On nested simple recursion

2011 ◽  
Vol 50 (5-6) ◽  
pp. 617-624 ◽  
Author(s):  
Ján Komara
Keyword(s):  
Simple Recursion

scholarly journals Finite Controllability for Ontology-Mediated Query Answering of CRPQ

2020 ◽  
Author(s):  
Diego Figueira ◽  
Santiago Figueira ◽  
Edwin Pin Baque
Keyword(s):  
Query Answering ◽  
Graph Structure ◽  
First Order ◽  
Underlying Graph ◽  
Graph Classes ◽  
Regular Path ◽  
Order Constraints ◽  
Simple Recursion ◽  
Regular Path Queries ◽  
Path Queries

Finite ontology mediated query answering (FOMQA) is the variant of ontology mediated query answering (OMQA) where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We study the property of finite-controllability, that is, whether FOMQA and OMQA are equivalent, for fragments of C2RPQ. C2RPQ is the language of conjunctive two-way regular path queries, which can be regarded as the result of adding simple recursion to Conjunctive Queries. For graph classes S, we consider fragments C2RPQ(S) of C2RPQ as the queries whose underlying graph structure is in S. We completely classify the finitely controllable and non-finitely controllable fragments under: inclusion dependencies, (frontier-)guarded rules, frontier-one rules (either with or without constants), and more generally under guarded-negation first-order constraints. For the finitely controllable fragments, we show a reduction to the satisfiability problem for guarded-negation first-order logic, yielding a 2EXPTIME algorithm (in combined complexity) for the corresponding (F)OMQA problem.

Comments on the Luria–Delbrück distribution

1994 ◽  
Vol 31 (3) ◽  
pp. 822-828 ◽  
Author(s):  
Adrienne W. Kemp
Keyword(s):  
Population Size ◽  
Poisson Distribution ◽  
Mutation Rate ◽  
Recursion Relation ◽  
Random Mutation ◽  
Numerical Studies ◽  
Current Population ◽  
Simple Recursion ◽  
Adaptation Hypothesis

The long-tailed Luria–Delbrück distribution arises in connection with the ‘random mutation’ hypothesis (whereas the ‘directed adaptation' hypothesis is thought to give a Poisson distribution). At time t the distribution depends on the parameter m = gNt/(a + g) where Nt is the current population size and g/(a + g) is the relative mutation rate (assumed constant). The paper identifies three models for the distribution in the existing literature and gives a fourth model. Ma et al. (1992) recently proved that there is a remarkably simple recursion relation for the Luria–Delbrück probabilities pn and found that asymptotically pn ≈ c/n2; their numerical studies suggested that c = 1 when the parameter m is unity. Cairns et al. (1988) had previously argued and shown numerically that Pn = Σj ≧ n Pj ≈ m/n. Here we prove that n(n + 1)pn < m(1 + 11m/30) for n = 1, 2, ···, and hence prove that as n becomes large n(n + 1)pn, ≈ m; the result mPn ≈ m follows immediately.

scholarly journals Recursions for Convolutions of Arithmetic Distributions

1985 ◽  
Vol 15 (2) ◽  
pp. 135-139 ◽  
Author(s):  
Nelson De Pril
Keyword(s):  
Compound Distributions ◽  
Arithmetic Distribution ◽  
Simple Recursion

AbstractA simple recursion for the n-fold convolution of an arithmetic distribution with itself is developed and its relation to Panjer's algorithm for compound distributions is shown.

Comments on the Luria–Delbrück distribution

1994 ◽  
Vol 31 (03) ◽  
pp. 822-828
Author(s):  
Adrienne W. Kemp
Keyword(s):  
Population Size ◽  
Poisson Distribution ◽  
Mutation Rate ◽  
Recursion Relation ◽  
Random Mutation ◽  
Numerical Studies ◽  
Current Population ◽  
Simple Recursion ◽  
Adaptation Hypothesis

The long-tailed Luria–Delbrück distribution arises in connection with the ‘random mutation’ hypothesis (whereas the ‘directed adaptation' hypothesis is thought to give a Poisson distribution). At time t the distribution depends on the parameter m = gNt/(a + g) where Nt is the current population size and g/(a + g) is the relative mutation rate (assumed constant). The paper identifies three models for the distribution in the existing literature and gives a fourth model. Ma et al. (1992) recently proved that there is a remarkably simple recursion relation for the Luria–Delbrück probabilities pn and found that asymptotically pn ≈ c/n 2; their numerical studies suggested that c = 1 when the parameter m is unity. Cairns et al. (1988) had previously argued and shown numerically that Pn = Σj ≧ n Pj ≈ m/n. Here we prove that n(n + 1)pn &lt; m(1 + 11m/30) for n = 1, 2, ···, and hence prove that as n becomes large n(n + 1)pn , ≈ m; the result mPn ≈ m follows immediately.

MOMENTS OF THE DURATION OF BUSY PERIODS OF MX/G/1/n SYSTEMS

2008 ◽  
Vol 22 (3) ◽  
pp. 347-354 ◽  
Author(s):  
António Pacheco ◽  
H. Ribeiro
Keyword(s):  
Arbitrary Number ◽  
Arbitrary Order ◽  
Simple Recursion ◽  
Number Of Customers

We derive a simple recursion to compute moments of arbitrary order of the duration of busy periods of MX/G/1/n systems starting with an arbitrary number of customers in the system.

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