A finitary approach for the representation of the infinitesimal generator of a markovian semigroup

2007 ◽  
pp. 170-176
Author(s):  
Schérazade Benhabib
Keyword(s):  
Infinitesimal Generator ◽  
Markovian Semigroup

scholarly journals Heat kernels of the discrete Laguerre operators

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Aleksey Kostenko
Keyword(s):  
Hardy Inequality ◽  
Jacobi Polynomials ◽  
Heat Kernels ◽  
The Other ◽  
Heat Semigroup ◽  
Stochastic Completeness ◽  
Markovian Semigroup ◽  
Other Hand ◽  
The One

AbstractFor the discrete Laguerre operators we compute explicitly the corresponding heat kernels by expressing them with the help of Jacobi polynomials. This enables us to show that the heat semigroup is ultracontractive and to compute the corresponding norms. On the one hand, this helps us to answer basic questions (recurrence, stochastic completeness) regarding the associated Markovian semigroup. On the other hand, we prove the analogs of the Cwiekel–Lieb–Rosenblum and the Bargmann estimates for perturbations of the Laguerre operators, as well as the optimal Hardy inequality.

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.

On the Roughness of Quasinilpotency Property of One-parameter Semigroups

2017 ◽  
Vol 60 (2) ◽  
pp. 364-371 ◽  
Author(s):  
Ciprian Preda
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Infinitesimal Generator ◽  
Autonomous Systems ◽  
Dynamical Systems Theory ◽  
Extinction Property ◽  
Quasinilpotent Operators ◽  
Strong Concept ◽  
Time Extinction

AbstractLet S := {S(t)}t≥0 be a C0-semigroup of quasinilpotent operators (i.e., σ(S(t)) = {0} for eacht> 0). In dynamical systems theory the above quasinilpotency property is equivalent to a very strong concept of stability for the solutions of autonomous systems. This concept is frequently called superstability and weakens the classical ûnite time extinction property (roughly speaking, disappearing solutions). We show that under some assumptions, the quasinilpotency, or equivalently, the superstability property of a C0-semigroup is preserved under the perturbations of its infinitesimal generator.

scholarly journals Necessary conditions of optimality for infinite dimensional uncertain systems

1995 ◽  
Vol 1 (3) ◽  
pp. 179-191 ◽  
Author(s):  
N. U. Ahmed ◽  
X. Xiang
Keyword(s):  
Uncertain Systems ◽  
Infinitesimal Generator ◽  
Continuous Semigroup ◽  
Computational Algorithm ◽  
Necessary Conditions ◽  
Reflexive Banach Space ◽  
Linear Operators ◽  
Infinite Dimensional ◽  
Necessary Conditions Of Optimality ◽  
Semigroup Of Linear Operators

In this paper we consider optimal control problem for infinite dimensional uncertain systems. Necessary conditions of optimality are presented under the assumption that the principal operator is the infinitesimal generator of a strongly continuous semigroup of linear operators in a reflexive Banach space. Further, a computational algorithm suitable for computing the optimal policies is also given.

scholarly journals The Randomized American Option as a Classical Solution to the Penalized Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Guillaume Leduc
Keyword(s):  
Cauchy Problem ◽  
Brownian Motion ◽  
Classical Solution ◽  
Penalty Method ◽  
Infinitesimal Generator ◽  
American Option ◽  
Geometric Brownian Motion ◽  
Uniform Bound ◽  
Option Value ◽  
The Cauchy Problem

We connect the exercisability randomized American option to the penalty method by showing that the randomized American option valueuis the uniqueclassicalsolution to the Cauchy problem corresponding to thecanonicalpenalty problem for American options. We also establish a uniform bound forAu, whereAis the infinitesimal generator of a geometric Brownian motion.

scholarly journals Dua Formula Eksponensial (Operator Linear dari Semigrup)

2021 ◽  
Vol 18 (1) ◽  
pp. 41-46
Author(s):  
L Meisaroh
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Infinitesimal Generator ◽  
The Other ◽  
Bounded Linear ◽  
Unbounded Linear Operator ◽  
C0 Semigroup

Assumed A is infinitesimal generator of C0-semigroup T(t) on X. This could be defined as T(t)=etA, applies if A is a bounded linear operator. Not if A is unbounded linear operator, then it will result in one possibility that show T(t) could be represented as etA. This paper will discuss and detail the proof of the other two formulas that show T(t) could be represented as etA.

Identifying Coefficients in the Spectral Representation for First Passage Time Distributions

1987 ◽  
Vol 1 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Mark Brown ◽  
Yi-Shi Shao
Keyword(s):  
Markov Processes ◽  
Time Distribution ◽  
Infinitesimal Generator ◽  
Spectral Representation ◽  
First Passage Time ◽  
Passage Time ◽  
Spectral Approach ◽  
Generator Matrix ◽  
Eigenvalues And Eigenvectors ◽  
First Passage

The spectral approach to first passage time distributions for Markov processes requires knowledge of the eigenvalues and eigenvectors of the infinitesimal generator matrix. We demonstrate that in many cases knowledge of the eigenvalues alone is sufficient to compute the first passage time distribution.

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