scholarly journals On a Comparison Result for Markov Processes

2008 ◽  
Vol 45 (01) ◽  
pp. 279-286
Author(s):  
Ludger Rüschendorf
Keyword(s):  
Markov Processes ◽  
Comparison Theorem ◽  
General Class ◽  
Stochastic Monotonicity ◽  
Comparison Result ◽  
State Spaces ◽  
Stochastic Orderings ◽  
Infinitesimal Generators ◽  
Real Functions

A comparison theorem is stated for Markov processes in Polish state spaces. We consider a general class of stochastic orderings induced by a cone of real functions. The main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators imply ordering of the processes. Several applications to convex type and to dependence orderings are given. In particular, Liggett's theorem on the association of Markov processes is a consequence of this comparison result.

scholarly journals On a Comparison Result for Markov Processes

2008 ◽  
Vol 45 (1) ◽  
pp. 279-286 ◽  
Author(s):  
Ludger Rüschendorf
Keyword(s):  
Markov Processes ◽  
Comparison Theorem ◽  
General Class ◽  
Stochastic Monotonicity ◽  
Comparison Result ◽  
State Spaces ◽  
Stochastic Orderings ◽  
Infinitesimal Generators ◽  
Real Functions

A comparison theorem is stated for Markov processes in Polish state spaces. We consider a general class of stochastic orderings induced by a cone of real functions. The main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators imply ordering of the processes. Several applications to convex type and to dependence orderings are given. In particular, Liggett's theorem on the association of Markov processes is a consequence of this comparison result.

MARKOV Processes in General State Spaces

1978 ◽  
Vol 86 (1) ◽  
pp. 67-83 ◽  
Author(s):  
H. J. Engelbert
Keyword(s):  
Markov Processes ◽  
General State ◽  
State Spaces

A Note on a Comparison Result for Elliptic Equations

1977 ◽  
Vol 29 (5) ◽  
pp. 1081-1085 ◽  
Author(s):  
W. Allegretto
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Comparison Theorem ◽  
Elliptic Equations ◽  
Comparison Result ◽  
Mixed Derivatives ◽  
Image Position ◽  
Derivatives Of

In a recent paper [2], Bushard established and applied a comparison theorem for positive solutions to the equation:in an arbitrary bounded domain D of Euclidean w-space Rn. The proof of these results depended on the absence of mixed derivatives of u in the equation considered.

scholarly journals Stochastic Monotonicity and Duality ofkth Order with Application to Put-Call Symmetry of Powered Options

2015 ◽  
Vol 52 (1) ◽  
pp. 82-101 ◽  
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Option Pricing ◽  
Markov Processes ◽  
Ruin Probability ◽  
Analytic Approach ◽  
Stochastic Monotonicity ◽  
Full Characterization

We introduce a notion ofkth order stochastic monotonicity and duality that allows us to unify the notion used in insurance mathematics (sometimes refereed to as Siegmund's duality) for the study of ruin probability and the duality responsible for the so-called put-call symmetries in option pricing. Our generalkth order duality can be interpreted financially as put-call symmetry for powered options. The main objective of this paper is to develop an effective analytic approach to the analysis of duality that will lead to the full characterization ofkth order duality of Markov processes in terms of their generators, which is new even for the well-studied case of put-call symmetries.

scholarly journals On the limiting spectral density of random matrices filled with stochastic processes

2019 ◽  
Vol 27 (2) ◽  
pp. 89-105 ◽  
Author(s):  
Matthias Löwe ◽  
Kristina Schubert
Keyword(s):  
Stochastic Process ◽  
Spectral Density ◽  
Random Matrices ◽  
Markov Processes ◽  
Random Matrix ◽  
Matrix Theory ◽  
Gibbs Measures ◽  
State Spaces ◽  
The Matrix ◽  
Finite State

Abstract We discuss the limiting spectral density of real symmetric random matrices. In contrast to standard random matrix theory, the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic process. Under assumptions on this process which are satisfied, e.g., by stationary Markov chains on finite sets, by stationary Gibbs measures on finite state spaces, or by Gaussian Markov processes, we show that the limiting spectral distribution depends on the way the matrix is filled with the stochastic process. If the filling is in a certain way compatible with the symmetry condition on the matrix, the limiting law of the empirical eigenvalue distribution is the well-known semi-circle law. For other fillings we show that the semi-circle law cannot be the limiting spectral density.

A comparison theorem for conditioned Markov processes

1991 ◽  
Vol 28 (01) ◽  
pp. 74-83 ◽  
Author(s):  
G. O. Roberts
Keyword(s):  
Markov Processes ◽  
Comparison Theorem ◽  
Hitting Time ◽  
Time Dependent ◽  
One Dimensional

Intuitively, the effect of conditioning a one-dimensional process to remain below a certain (possibly time-dependent) boundary is to ‘push' the process downwards. This paper investigates the effect of such conditioning, and finds the class of processes for which our intuition is accurate. It is found that ordinary stochastic inequalities are in general unsuitable for making statements about such conditioned processes, and that a stronger type of inequality is more appropriate. The investigation is motivated by applications in estimation of boundary hitting time distributions.

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