Comparison between Numerical and Simulation Methods for Age-dependent Branching Models with Immigration

2000 Mathematics Subject Classification: primary: 60J80, 60J85, secondary: 62M09, 92D40

Nonparametric Estimation in the Class of Bisexual Processes with Population-Size Dependent Mating

2000 Mathematics Subject Classification: 60J80, 62M05

Estimation of the Offspring Mean in a General Single-Type Size-Dependent Branching Process

2000 Mathematics Subject Classification: 60J80, 62F12, 62P10

Total Progeny in a Subcritical Branching Process with two Types of Immigration

2000 Mathematics Subject Classification: 60J80, 60F05

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

Monsoon circulation interaction with Western Ghats orography under changing climate - Projection by a 20-km mesh AGCM

In this study, the authors have investigated the likely future changes in the summer monsoon over the Western Ghats (WG) orographic region of India in response to global warming, using time-slice simulations of an ultra high-resolution global climate model and climate datasets of recent past. The model with approximately 20-km mesh horizontal resolution resolves orographic features on finer spatial scales leading to a quasi-realistic simulation of the spatial distribution of the present-day summer monsoon rainfall over India and trends in monsoon rainfall over the west coast of India. As a result, a higher degree of confidence appears to emerge in many aspects of the 20-km model simulation, and therefore, we can have better confidence in the validity of the model prediction of future changes in the climate over WG mountains. Our analysis suggests that the summer mean rainfall and the vertical velocities over the orographic regions of Western Ghats have significantly weakened during the recent past and the model simulates these features realistically in the present-day climate simulation. Under future climate scenario, by the end of the twenty-first century, the model projects reduced orographic precipitation over the narrow Western Ghats south of 16A degrees N that is found to be associated with drastic reduction in the southwesterly winds and moisture transport into the region, weakening of the summer mean meridional circulation and diminished vertical velocities. We show that this is due to larger upper tropospheric warming relative to the surface and lower levels, which decreases the lapse rate causing an increase in vertical moist static stability (which in turn inhibits vertical ascent) in response to global warming. Increased stability that weakens vertical velocities leads to reduction in large-scale precipitation which is found to be the major contributor to summer mean rainfall over WG orographic region. This is further corroborated by a significant decrease in the frequency of moderate-to-heavy rainfall days over WG which is a typical manifestation of the decrease in large-scale precipitation over this region. Thus, the drastic reduction of vertical ascent and weakening of circulation due to `upper tropospheric warming effect' predominates over the `moisture build-up effect' in reducing the rainfall over this narrow orographic region. This analysis illustrates that monsoon rainfall over mountainous regions is strongly controlled by processes and parameterized physics which need to be resolved with adequately high resolution for accurate assessment of local and regional-scale climate change.

The estimation of stochastic context-free grammars using the Inside-Outside algorithm

Using an entropy argument, it is shown that stochastic context-free grammars (SCFG's) can model sources with hidden branching processes more efficiently than stochastic regular grammars (or equivalently HMM's). However, the automatic estimation of SCFG's using the Inside-Outside algorithm is limited in practice by its O(n3) complexity. In this paper, a novel pre-training algorithm is described which can give significant computational savings. Also, the need for controlling the way that non-terminals are allocated to hidden processes is discussed and a solution is presented in the form of a grammar minimization procedure. © 1990.

Applications of Feller-Reuter-Riley transition functions

A Feller–Reuter–Riley function is a Markov transition function whose corresponding semigroup maps the set of the real-valued continuous functions vanishing at infinity into itself. The aim of this paper is to investigate applications of such functions in the dual problem, Markov branching processes, and the Williams-matrix. The remarkable property of a Feller–Reuter–Riley function is that it is a Feller minimal transition function with a stable q-matrix. By using this property we are able to prove that, in the theory of branching processes, the branching property is equivalent to the requirement that the corresponding transition function satisfies the Kolmogorov forward equations associated with a stable q-matrix. It follows that the probabilistic definition and the analytic definition for Markov branching processes are actually equivalent. Also, by using this property, together with the Resolvent Decomposition Theorem, a simple analytical proof of the Williams' existence theorem with respect to the Williams-matrix is obtained. The close link between the dual problem and the Feller–Reuter–Riley transition functions is revealed. It enables us to prove that a dual transition function must satisfy the Kolmogorov forward equations. A necessary and sufficient condition for a dual transition function satisfying the Kolmogorov backward equations is also provided.

Strong ergodicity of monotone transition functions

By revealing close links among strong ergodicity, monotone, and the Feller–Reuter–Riley (FRR) transition functions, we prove that a monotone ergodic transition function is strongly ergodic if and only if it is not FRR. An easy to check criterion for a Feller minimal monotone chain to be strongly ergodic is then obtained. We further prove that a non-minimal ergodic monotone chain is always strongly ergodic. The applications of our results are illustrated using birth-and-death processes and branching processes.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Ecuaciones diferenciales estocásticas con condición final y soluciones de viscosidad de EDPS semilineales de segundo orden

El objetivo de este documento es recopilar algunos resultados clasicos sobre existencia y unicidad ´ de soluciones de ecuaciones diferenciales estocasticas (EDEs) con condici ´ on final (en ingl ´ es´ Backward stochastic differential equations) con particular enfasis en el caso de coeficientes mon ´ otonos, y su cone- ´ xion con soluciones de viscosidad de sistemas de ecuaciones diferenciales parciales (EDPs) parab ´ olicas ´ y el´ıpticas semilineales de segundo orden.

Direct time-resolved study of the gas-phase reactions of germylene with ethyl- and diethylgermane: absolute rate constants, temperature dependences, and mechanism

Time-resolved studies of germylene, GeH2, generated by the 193 nm laser flash photolysis of 3,4-dimethyl-1-germacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reactions with ethyl- and diethylgermanes in the gas phase. The reactions were studied over the pressure range 1-100 Torr with SF6 as bath gas and at five temperatures in the range 297-564 K. Only slight pressure dependences were found for GeH2 + EtGeH3 (399, 486, and 564 K). The high pressure rate constants gave the following Arrhenius parameters: for GeH2 + EtGeH3, log A = -10.75 +/- 0.08 and E-a = -6.7 +/- 0.6 kJ mol(-1); for GeH2 + Et2GeH2, log A = -10.68 +/- 0.11 and E-a = -6.95 +/- 0.80 kJ mol(-1). These are consistent with fast, near collision-controlled, association processes at 298 K. RRKM modeling calculations are, for the most part, consistent with the observed pressure dependence of GeH2 + EtGeH3. The ethyl substituent effects have been extracted from these results and are much larger than the analogous methyl substituent effects in the SiH2 + methylsilane reaction series. This is consistent with a mechanistic model for Ge-H insertion in which the intermediate complex has a sizable secondary barrier to rearrangement.

Gas phase kinetic and quantum chemical studies of the reactions of silylene with the methylsilanes. Absolute rate constants, temperature dependences, RRKM modelling and potential energy surfaces

Time resolved studies of silylene, SiH2, generated by the 193 nm laser. ash photolysis of phenylsilane, have been carried out to obtain rate coefficients for its bimolecular reactions with methyl-, dimethyl- and trimethyl-silanes in the gas phase. The reactions were studied over the pressure range 3 - 100 Torr with SF6 as bath gas and at five temperatures in the range 300 - 625 K. Only slight pressure dependences were found for SiH2 + MeSiH3 ( 485 and 602 K) and for SiH2 + Me2SiH2 ( 600 K). The high pressure rate constants gave the following Arrhenius parameters: [GRAPHICS] These are consistent with fast, near to collision-controlled, association processes. RRKM modelling calculations are consistent with the observed pressure dependences ( and also the lack of them for SiH2 + Me3SiH). Ab initio calculations at both second order perturbation theory (MP2) and coupled cluster (CCSD(T)) levels, showed the presence of weakly-bound complexes along the reaction pathways. In the case of SiH2 + MeSiH3 two complexes, with different geometries, were obtained consistent with earlier studies of SiH2 + SiH4. These complexes were stabilised by methyl substitution in the substrate silane, but all had exceedingly low barriers to rearrangement to product disilanes. Although methyl groups in the substrate silane enhance the intrinsic SiH2 insertion rates, it is doubtful whether the intermediate complexes have a significant effect on the kinetics. A further calculation on the reaction MeSiH + SiH4 shows that the methyl substitution in the silylene should have a much more significant kinetic effect ( as observed in other studies).

Markov Constraints for Generating Texts with Style

This thesis addresses the issue of generating texts in the style of an existing author, that also satisfy structural constraints imposed by the genre of the text. Although Markov processes are known to be suitable for representing style, they are difficult to control in order to satisfy non-local properties, such as structural constraints, that require long distance modeling. The framework of Constrained Markov Processes allows to precisely generate texts that are consistent with a corpus, while being controllable in terms of rhymes and meter. Controlled Markov processes consist in reformulating Markov processes in the context of constraint satisfaction. The thesis describes how to represent stylistic and structural properties in terms of constraints in this framework and how this approach can be used for the generation of lyrics in the style of 60 differents authors An evaluation of the desctibed method is provided by comparing it to both pure Markov and pure constraint-based approaches. Finally the thesis describes the implementation of an augmented text editor, called Perec. Perec is intended to improve creativity, by helping the user to write lyrics and poetry, exploiting the techniques presented so far.