scholarly journals THE APPLICABILITY OF FINITE HOMOGENEOUS MARKOV PROCESSES IN THE STUDY OF CONSUMER LOYALTY

2021 ◽  
pp. 200-206
Author(s):  
Dr Swapna Datta Khan
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Finite Time ◽  
Transition Matrix ◽  
Switching Time ◽  
Consumer Loyalty ◽  
Brand Switching ◽  
Previous Event ◽  
Fast Moving Consumer Goods ◽  
Conceptual Paper

Markov Processes are sequential events that are related to each other stochastically. Such events, also known as states, may be such that the probability of an event occurring depends only on the previous event and not on any event prior to that. This is known as the memoryless property of Markov Processes. Certain dynamic market conditions especially with respect to the Fast-Moving Consumer Goods Sector, the Telecommunications Sector may enable the use of finite and time-homogeneous Markov Processes to study the brand switching tendency of the consumer, and thus predict consumer loyalty. In this conceptual paper, we shall study how to predict brand switching tendencies using finite, time-homogeneous Markov Processes. KEYWORDS: Markov Process, Brand Switching, Time-Homogeneous, Consumer Loyalty, Transition Matrix

Order and Homogeneity of Family Specific Brand-switching Processes

1966 ◽  
Vol 3 (1) ◽  
pp. 48-54 ◽  
Author(s):  
William F. Massy
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Transition Probability ◽  
Empirical Work ◽  
Brand Choice ◽  
First Order ◽  
Brand Switching ◽  
Transition Probability Matrices ◽  
Probability Matrices ◽  
Crucial Assumption

Most empirical work on Markov processes for brand choice has been based on aggregative data. This article explores the validity of the crucial assumption that underlies such analyses, i.e., that all the families in the sample follow a Markov process with the same or similar transition probability matrices. The results show that there is a great deal of diversity among families’ switching processes, and that many of them are of zero rather than first order.

ACCELERATING MONTE CARLO MARKOV PROCESSES

COSMOS ◽  
2005 ◽  
Vol 01 (01) ◽  
pp. 87-94 ◽  
Author(s):  
CHII-RUEY HWANG
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Process ◽  
Markov Processes ◽  
Transition Matrix ◽  
Asymptotic Variance ◽  
Suitable Condition ◽  
Transition Matrices ◽  
Finite Set ◽  
The Continuum

Let π be a probability density proportional to exp - U(x) in S. A convergent Markov process to π(x) may be regarded as a "conceptual" algorithm. Assume that S is a finite set. Let X0,X1,…,Xn,… be a Markov chain with transition matrix P and invariant probability π. Under suitable condition on P, it is known that [Formula: see text] converges to π(f) and the corresponding asymptotic variance v(f, P) depends only on f and P. It is natural to consider criteria vw(P) and va(P), defined respectively by maximizing and averaging v(f, P) over f. Two families of transition matrices are considered. There are four problems to be investigated. Some results and conjectures are given. As for the continuum case, to accelerate the convergence a family of diffusions with drift ∇U(x) + C(x) with div(C(x)exp - U(x)) = 0 is considered.

scholarly journals CLASSICAL MARKOV PROCESSES FROM QUANTUM LÉVY PROCESSES

1999 ◽  
Vol 02 (01) ◽  
pp. 105-129 ◽  
Author(s):  
UWE FRANZ
Keyword(s):  
Markov Process ◽  
Hopf Algebra ◽  
Markov Processes ◽  
Lévy Processes ◽  
Sufficient Conditions ◽  
Markov Property ◽  
Vacuum State ◽  
Levy Processes ◽  
Quantum Process ◽  
Quantum Markov Processes

We show how classical Markov processes can be obtained from quantum Lévy processes. It is shown that quantum Lévy processes are quantum Markov processes, and sufficient conditions for restrictions to subalgebras to remain quantum Markov processes are given. A classical Markov process (which has the same time-ordered moments as the quantum process in the vacuum state) exists whenever we can restrict to a commutative subalgebra without losing the quantum Markov property.8 Several examples, including the Azéma martingale, with explicit calculations are presented. In particular, the action of the generator of the classical Markov processes on polynomials or their moments are calculated using Hopf algebra duality.

A temporal factorization at the maximum for certain positive self-similar Markov processes

2020 ◽  
Vol 57 (4) ◽  
pp. 1045-1069
Author(s):  
Matija Vidmar
Keyword(s):  
Markov Process ◽  
Laplace Transform ◽  
Markov Processes ◽  
Absorption Time ◽  
The Laplace Transform ◽  
Self Similar

AbstractFor a spectrally negative self-similar Markov process on $[0,\infty)$ with an a.s. finite overall supremum, we provide, in tractable detail, a kind of conditional Wiener–Hopf factorization at the maximum of the absorption time at zero, the conditioning being on the overall supremum and the jump at the overall supremum. In a companion result the Laplace transform of this absorption time (on the event that the process does not go above a given level) is identified under no other assumptions (such as the process admitting a recurrent extension and/or hitting zero continuously), generalizing some existing results in the literature.

scholarly journals Analyzing proprietary, private label, and non-brands in fresh produce purchases

2020 ◽  
pp. 147078532094833 ◽  
Author(s):  
Zachary William Anesbury ◽  
Kristin Jürkenbeck ◽  
Timofei Bogomolov ◽  
Svetlana Bogomolova
Keyword(s):  
United States ◽  
Fruits And Vegetables ◽  
Fresh Produce ◽  
The United States ◽  
Private Label ◽  
Consumer Loyalty ◽  
Buying Behavior ◽  
Fast Moving Consumer Goods ◽  
Private Label Brands ◽  
Analytical Approaches

When purchasing packaged products within a supermarket, consumers choose between proprietary or private label brands. However, when purchasing fresh fruits and vegetables, non-branded produce is the dominant option—with proprietary and private label brands only recently becoming available. Previous fast-moving consumer goods (FMCG) research finds that proprietary and private label brands affect consumer loyalty—however, no research exists for fresh categories. This research is the first to determine the effect of emerging brands in fresh categories on consumer buying behavior. Our research examines consumers’ loyalty toward proprietary, private label, or non-branded fresh fruits and vegetables and the level of customer sharing between these options, using analytical approaches applicable to FMCG categories. The panel data contains nearly 46,000 households making over 8 million purchases in the United States during 2015. Results show that proprietary, private label, and now non-branded fresh produce have expected loyalty levels, for their size, and consumers share their purchases across the three options (i.e., consumers are not loyal to just one option). The study analyzes and interprets purchase data in fresh categories offering marketing academics and practitioners actionable advice for working with fresh produce purchase data.

Extension of Wald's first lemma to Markov processes

1999 ◽  
Vol 36 (01) ◽  
pp. 48-59 ◽  
Author(s):  
George V. Moustakides
Keyword(s):  
Integral Equation ◽  
Markov Process ◽  
Markov Processes ◽  
Correction Term ◽  
Stopping Time ◽  
Poisson Integral ◽  
Homogeneous Markov Process ◽  
Partial Sum ◽  
Poisson Integral Equation ◽  
Scalar Nonlinearity

Let ξ0,ξ1,ξ2,… be a homogeneous Markov process and let S n denote the partial sum S n = θ(ξ1) + … + θ(ξ n ), where θ(ξ) is a scalar nonlinearity. If N is a stopping time with 𝔼N < ∞ and the Markov process satisfies certain ergodicity properties, we then show that 𝔼S N = [lim n→∞𝔼θ(ξ n )]𝔼N + 𝔼ω(ξ0) − 𝔼ω(ξ N ). The function ω(ξ) is a well defined scalar nonlinearity directly related to θ(ξ) through a Poisson integral equation, with the characteristic that ω(ξ) becomes zero in the i.i.d. case. Consequently our result constitutes an extension to Wald's first lemma for the case of Markov processes. We also show that, when 𝔼N → ∞, the correction term is negligible as compared to 𝔼N in the sense that 𝔼ω(ξ0) − 𝔼ω(ξ N ) = o(𝔼N).

Composable Markov processes

1970 ◽  
Vol 7 (2) ◽  
pp. 400-410 ◽  
Author(s):  
Tore Schweder
Keyword(s):  
Social Sciences ◽  
Markov Process ◽  
Markov Processes ◽  
Infinitesimal Generator ◽  
A Priori ◽  
The Social

Many phenomena studied in the social sciences and elsewhere are complexes of more or less independent characteristics which develop simultaneously. Such phenomena may often be realistically described by time-continuous finite Markov processes. In order to define such a model which will take care of all the relevant a priori information, there ought to be a way of defining a Markov process as a vector of components representing the various characteristics constituting the phenomenon such that the dependences between the characteristics are represented by explicit requirements on the Markov process, preferably on its infinitesimal generator.

scholarly journals On invariant measures of nonlinear Markov processes

1993 ◽  
Vol 6 (4) ◽  
pp. 385-406 ◽  
Author(s):  
N. U. Ahmed ◽  
Xinhong Ding
Keyword(s):  
Markov Process ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Markov Processes ◽  
Existence And Uniqueness ◽  
Invariant Measures ◽  
Nonlinear Markov Processes

We consider a nonlinear (in the sense of McKean) Markov process described by a stochastic differential equations in Rd. We prove the existence and uniqueness of invariant measures of such process.

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