scholarly journals Inhomogeneous Random Evolutions: Limit Theorems and Financial Applications

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 447 ◽  
Author(s):  
Nelson Vadori ◽  
Anatoliy Swishchuk
Keyword(s):  
Regime Switching ◽  
Limit Theorems ◽  
Switching Time ◽  
Price Impact ◽  
Diffusion Limit ◽  
Price Dynamics ◽  
Financial Applications ◽  
Large Numbers ◽  
Random Evolutions ◽  
Limit Result

The paper is devoted to the inhomogeneous random evolutions (IHRE) and their applications in finance. We introduce and present some properties of IHRE. Then, we prove weak law of large numbers and central limit theorems for IHRE. Financial applications are given to illiquidity modeling using regime-switching time-inhomogeneous Levy price dynamics, to regime-switching Levy driven diffusion based price dynamics, and to a generalized version of the multi-asset model of price impact from distress selling, for which we retrieve and generalize their diffusion limit result for the price process.

scholarly journals Limit theorems for multi-type general branching processes with population dependence

2020 ◽  
Vol 52 (4) ◽  
pp. 1127-1163
Author(s):  
Jie Yen Fan ◽  
Kais Hamza ◽  
Peter Jagers ◽  
Fima C. Klebaner
Keyword(s):  
Carrying Capacity ◽  
Population Model ◽  
General Framework ◽  
Limit Theorems ◽  
Mating Systems ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Special Section ◽  
Large Numbers ◽  
Type Population

AbstractA general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the population as a measure-valued process and obtain its asymptotics as the population grows with the environmental carrying capacity. Thus, a deterministic approximation is given, in the form of a law of large numbers, as well as a central limit theorem. This general framework is then adapted to model sexual reproduction, with a special section on serial monogamic mating systems.

scholarly journals Subcritical Sevastyanov branching processes with nonhomogeneous Poisson immigration

2017 ◽  
Vol 54 (2) ◽  
pp. 569-587 ◽  
Author(s):  
Ollivier Hyrien ◽  
Kosto V. Mitov ◽  
Nikolay M. Yanev
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Cell Populations ◽  
Subcritical Case ◽  
Immigration Process ◽  
Large Numbers

Abstract We consider a class of Sevastyanov branching processes with nonhomogeneous Poisson immigration. These processes relax the assumption required by the Bellman–Harris process which imposes the lifespan and offspring of each individual to be independent. They find applications in studies of the dynamics of cell populations. In this paper we focus on the subcritical case and examine asymptotic properties of the process. We establish limit theorems, which generalize classical results due to Sevastyanov and others. Our key findings include a novel law of large numbers and a central limit theorem which emerge from the nonhomogeneity of the immigration process.

The Erdős–Rényi Law and Strong Limit Theorems of Probability

2021 ◽  
Vol 58 (2) ◽  
pp. 263-273
Author(s):  
Andrei N. Frolov
Keyword(s):  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Strong Limit ◽  
Large Numbers ◽  
Famous Paper

Fifty years ago P. Erdős and A. Rényi published their famous paper on the new law of large numbers. In this survey, we describe numerous results and achievements which are related with this paper or motivated by it during these years.

Limit Theorems for Random Evolutions

1997 ◽  
pp. 61-102
Author(s):  
Anatoly Swishchuk
Keyword(s):  
Limit Theorems ◽  
Random Evolutions

Limit theorems for loss networks with diverse routing

1989 ◽  
Vol 21 (04) ◽  
pp. 804-830 ◽  
Author(s):  
I. B. Ziedins ◽  
F.P. Kelly
Keyword(s):  
Information Systems ◽  
Asymptotic Analysis ◽  
Limit Theorems ◽  
Loss Networks ◽  
Exact Analysis ◽  
Large Numbers

Loss networks have long been of interest to telephone engineers, and are becoming increasingly important as models of computer and information systems. In this paper we present an asymptotic analysis of loss networks exhibiting various forms of symmetry. Our aim is to better understand the behaviour of networks involving very large numbers of links and routes, where an exact analysis is not possible and approximations are required.

SOME LIMIT THEOREMS OF DELAYED AVERAGES FOR COUNTABLE NONHOMOGENEOUS MARKOV CHAINS

2019 ◽  
pp. 1-19
Author(s):  
Pingping Zhong ◽  
Weiguo Yang ◽  
Zhiyan Shi ◽  
Yan Zhang
Keyword(s):  
Information Theory ◽  
Markov Chains ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
Strong Ergodicity ◽  
Large Numbers ◽  
Nonhomogeneous Markov Chains ◽  
Definition Of ◽  
Bivariate Functions

AbstractThe purpose of this paper is to establish some limit theorems of delayed averages for countable nonhomogeneous Markov chains. The definition of the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for countable nonhomogeneous Markov chains is introduced first. Then a theorem about the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for the nonhomogeneous Markov chains is established, and its applications to the information theory are given. Finally, the strong law of large numbers of delayed averages of bivariate functions for countable nonhomogeneous Markov chains is proved.

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