Related papers: Generalized crested products of Markov chains
For a finite group $G$, a $G$-crossed braided fusion category is $G$-graded fusion category with additional structures, namely a $G$-action and a $G$-braiding. We develop the notion of $G$-crossed braided zesting: an explicit method for…
Enlargement of filtrations is a classical topic in the general theory of stochastic processes. This theory has been applied to stochastic finance in order to analyze models with insider information. In this paper we study initial…
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…
The conventional perspective on Markov chains considers decision problems concerning the probabilities of temporal properties being satisfied by traces of visited states. However, consider the following query made of a stochastic system…
An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that works for general state space Markov chains under very general…
We generalize graded Hecke algebras to include a twisting two-cocycle for the associated finite group. We give examples where the parameter spaces of the resulting twisted graded Hecke algebras are larger than that of the graded Hecke…
For a relatively large class of well-behaved absorbing (or killed) finite Markov chains, we give detailed quantitative estimates regarding the behavior of the chain before it is absorbed (or killed). Typical examples are random walks on…
We study a large class of reversible Markov chains with discrete state space and transition matrix $P_N$. We define the notion of a set of {\it metastable points} as a subset of the state space $\G_N$ such that (i) this set is reached from…
The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in…
We consider a type of Markov property for set-indexed processes which is satisfied by all processes with independent increments and which allows us to introduce a transition system theory leading to the construction of the process. A…
A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness allows one to lift most good properties from finite Markov chains to denumerable…
We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…
In this paper, we first introduce and define several new information divergences in the space of transition matrices of finite Markov chains which measure the discrepancy between two Markov chains. These divergences offer natural…
Adopting a purely group-theoretical point of view, we consider the star product of functions which is associated, in a natural way, with a square integrable (in general, projective) representation of a locally compact group. Next, we show…
We define the twisted tensor product of two enriched categories, which generalizes various sorts of `products' of algebraic structures, including the bicrossed product of groups, the twisted tensor product of (co)algebras and the double…
This article proposes a new generalization of the Multivariate Markov Chains (MMC) model. The future values of a Markov chain commonly depend on only the past values of the chain in an autoregressive fashion. The generalization proposed in…
There exists a range of different models for estimating and simulating credit risk transitions to optimally manage credit risk portfolios and products. In this chapter we present a Coupled Markov Chain approach to model rating transitions…
In extreme value statistics, the peaks-over-threshold method is widely used. The method is based on the generalized Pareto distribution characterizing probabilities of exceedances over high thresholds in $\mathbb {R}^d$. We present a…
We consider a stochastic model of gene expression in which transcription depends on a multistate promoter, including the famous two-state model and refractory promoters as special cases, and focus on deriving the exact stationary…
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…