843 research outputs found
Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations
No full textThe small diffusion and fast dying out asymptotics is calculated for nonlinear evolution
equations of a class of superprocesses on manifolds, and the corresponding logarithmic limit
of the solution is shown to be given by a solution of a certain problem of calculus of variations
with a non-additive (and non-integral) functional
Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations
No full textWe study stochastic Hamilton-Jacobi-Bellman equations and the
corresponding Hamiltonian systems driven by jump-type Lévy processes.
The main objective of the present paper is to show existence,
uniqueness and a (locally in time) diffeomorphism property of the solution:
the solution trajectory of the system is a diffeomorphism as a
function of the initial momentum. This result enables us to implement
a stochastic version of the classical method of characteristics for the
Hamilton-Jacobi equations. An –in itself interesting– auxiliary result
are pointwise a.s. estimates for iterated stochastic integrals driven by
a vector of not necessarily independent jump-type semimartingales
Idempotent structures in optimization
No full textConsider the set A = R ∪ {+∞} with the binary operations o1 = max
and o2 = + and denote by An the set of vectors v = (v1,...,vn) with entries
in A. Let the generalised sum u o1 v of two vectors denote the vector with
entries uj o1 vj , and the product a o2 v of an element a ∈ A and a vector
v ∈ An denote the vector with the entries a o2 vj . With these operations,
the set An provides the simplest example of an idempotent semimodule.
The study of idempotent semimodules and their morphisms is the subject
of idempotent linear algebra, which has been developing for about
40 years already as a useful tool in a number of problems of discrete optimisation.
Idempotent analysis studies infinite dimensional idempotent
semimodules and is aimed at the applications to the optimisations problems
with general (not necessarily finite) state spaces. We review here
the main facts of idempotent analysis and its major areas of applications
in optimisation theory, namely in multicriteria optimisation, in turnpike
theory and mathematical economics, in the theory of generalised solutions
of the Hamilton-Jacobi Bellman (HJB) equation, in the theory of games
and controlled Marcov processes, in financial mathematics
Stochastic monotonicity and duality for one-dimensional Markov processes
No full textThe theory of monotonicity and duality is developed for general one-dimensional
Feller processes, extending the approach from [11]. Moreover it is shown that local monotonicity conditions (conditions on the Lévy kernel) are sufficient to prove
the well-posedness of the corresponding Markov semigroup and process, including
unbounded coefficients and processes on the half-line
Nonlinear Markov semigroups and interacting Lévy type processes
No full textSemigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space R-d (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models
Stochastic evolution as a quasiclassical limit of a boundary value problem for Schrödinger equations
No full textWe develop systematically a new unifying approach to the analysis of
linear stochastic, quantum stochastic and even deterministic equations in
Banach spaces. Solutions to a wide class of these equations (in particular those decribing the processes of continuous quantum measurements)
are proved to coincide with the interaction representations of the solutions to certain Dirac type equations with boundary conditions in pseudo
Fock spaces. The latter are presented as the semi-classical limit of an appropriately dressed unitary evolutions corresponding to a boundary-value
problem for rather general Schrödinger equations with bounded below
Hamiltonians
The moscovite Conquest of Novgorod in V.N. Tatishchev’s Interpretation
No full textСтатья посвящена проблеме изучения взглядов В.Н. татищева на процесс централизации при Иване III, на примере присоединения Новгорода к Москве. автор приходит к выводу, что данные исторические события В.Н. татищев интерпретирует через восприятие им существующих форм правления и свои представления об их достоинствах и недостатках.The article studies the views of V.N. Tatishchev on the process of centralization under Ivan III, using the annexation of Novgorod to Moscow. The author concludes that V.N. Tatishchev interprets these historical events through his perception of existing forms of government and his ideas about their advantages and disadvantages
Problem of Sources in Researching V.N. Khitrovo’s Biography
No full textThrough their work, the author examines some of the problems of studying sources while researching the biography of famous Russian statesman V.N. Khitrovo (1834-1903), who played an important role in shaping the Middle East foreign policy of the Russian Empire. While in the region, he made a great contribution to the protection of Orthodoxy and Orthodox pilgrims in the Holy Land, including the development of education of the Arab population of Palestine and Syria, and promoting the spread of Orthodox education. In order to reconstruct the biography of V.N. Khitrovo, sources of various nature and origin were identified and classified. There has been conducted for the first-time analysis of materials from the private collection of V.N. Khitrovo stored in the Department of Manuscripts of the Russian State Library; on their basis, the role of V.N. Khitrovo as a specialist in the field of genealogy is revealed within the text. The materials on the history of the Khitrovo family collected by him make it possible to most fully present the history of the family and its role in the development of the future statesman and organizer of science. There was used a wide range of unpublished archival documents containing material important for the reconstruction of V.N. Khitrovo’s biography. Above all, it is the correspondence of widow S.D. Khitrovo with bibliographer and literary critic S.I. Ponomarev. In addition, for the first time, the authors have collected obituary materials, a large amount of reference literature published in Russia in the second half of the XIX - early XX centuries, published official sources and documents of private origin, which have allow the researchers to begin supplementing, clarifying and correcting the information and facts from V.N. Khitrovo’s biography
External Pressure on Alliances: What Does the Prisoners’ Dilemma Reveal?
No full textPrompted by a real-life observation in the UK retail market, a two-player Prisoners’ Dilemma model of an alliance between two firms is adapted to include the response of a rival firm, resulting in a version of a three-player Prisoners’ Dilemma. We use this to analyse the impact on the stability of the alliance of the rival’s competition, either with the alliance or with the individual partners. We show that, while strong external pressure on both partners can cause Ally-Ally to become a Nash equilibrium for the two-player Prisoners’ Dilemma, weak or asymmetric pressure that plays on the partners’ differing objectives can undermine the alliance. As well as providing new insights into how allies should respond if the alliance is to continue, this also illustrates how a third party can most effectively cause the alliance to become unsustainable. We create a new game theoretic framework, adding value to existing theory and the practice of alliance formation and sustainability
TEXStrict Nash equilibria in a duopolistic market share model
No full textThis paper develops a duopolistic discounted marketing model with linear advertising costs and advertised prices for mature markets still in expansion. Generic and predatory advertising eects are combined together in the model. We characterise a class of advertising models with some eciency for production costs. For such a class of models, advertising investments have a no-free-riding strict Nash equilibrium in pure strategies if discount rates are small. We discuss the entity of this eciency at varying of parameters of our advertising model. We provide a computational framework in which market shares can be computed at equilibrium, too. We analyse market share dynamics for an asymmetrical numerical scenario where one of the two rms is more eective in generic andpredatory advertising. Several numerical insights on market share dynamics are obtained. Our computational framework allows for dierent scenarios in practical applications and it is developed using the Mathematica software. We provide rational insights on how competing rms might ultimately reduce the qualityof manufactured goods when they publish the prices at the beginning of marketing campaigns
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