The stepwise time dependent backward kolmogorov equation with delayed neutrons in counting statistics

1981 ◽  
Vol 190 (3) ◽  
pp. 583-591 ◽  
Author(s):  
F. Carloni ◽  
M. Marseguerra
Keyword(s):  
Time Dependent ◽  
Kolmogorov Equation ◽  
Delayed Neutrons ◽  
Backward Kolmogorov Equation ◽  
Counting Statistics

scholarly journals The nonlocal boundary value problem for one-dimensional backward Kolmogorov equation and associated semigroup

2019 ◽  
Vol 11 (2) ◽  
pp. 463-474
Author(s):  
R.V. Shevchuk ◽  
I.Ya. Savka ◽  
Z.M. Nytrebych
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Boundary Integral ◽  
Kolmogorov Equation ◽  
Linear Parabolic Equation ◽  
One Dimensional ◽  
Wentzell Boundary Condition ◽  
Backward Kolmogorov Equation

This paper is devoted to a partial differential equation approach to the problem of construction of Feller semigroups associated with one-dimensional diffusion processes with boundary conditions in theory of stochastic processes. In this paper we investigate the boundary-value problem for a one-dimensional linear parabolic equation of the second order (backward Kolmogorov equation) in curvilinear bounded domain with one of the variants of nonlocal Feller-Wentzell boundary condition. We restrict our attention to the case when the boundary condition has only one term and it is of the integral type. The classical solution of the last problem is obtained by the boundary integral equation method with the use of the fundamental solution of backward Kolmogorov equation and the associated parabolic potentials. This solution is used to construct the Feller semigroup corresponding to such a diffusion phenomenon that a Markovian particle leaves the boundary of the domain by jumps.

scholarly journals On Deterministic and Stochastic Multiple Pathogen Epidemic Models

Epidemiologia ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 325-337
Author(s):  
Fernando Vadillo
Keyword(s):  
Variable Coefficients ◽  
Epidemic Models ◽  
Kolmogorov Equation ◽  
The Finite Element Method ◽  
Persistence Time ◽  
Main Challenge ◽  
Stochastic Epidemic ◽  
The Mean ◽  
Backward Kolmogorov Equation ◽  
Multiple Pathogen

In this paper, we consider a stochastic epidemic model with two pathogens. In order to analyze the coexistence of two pathogens, we compute numerically the expectation time until extinction (the mean persistence time), which satisfies a stationary partial differential equation with degenerate variable coefficients, related to backward Kolmogorov equation. I use the finite element method in order to solve this equation, and we implement it in FreeFem++. The main conclusion of this paper is that the deterministic and stochastic epidemic models differ considerably in predicting coexistence of the two diseases and in the extinction outcome of one of them. Now, the main challenge would be to find an explanation for this result.

Solution to the Backward-Kolmogorov Equation for a Nonstationary Oscillation Problem

1982 ◽  
Vol 49 (4) ◽  
pp. 923-925 ◽  
Author(s):  
G. P. Solomos ◽  
P-T. D. Spanos
Keyword(s):  
Random Excitation ◽  
Response Amplitude ◽  
Kolmogorov Equation ◽  
Linear Oscillator ◽  
Markov Approximation ◽  
Nonstationary Oscillation ◽  
Oscillation Problem ◽  
Backward Kolmogorov Equation

The solution of a backward-Kolmogorov equation is presented. This equation is associated with a Markov approximation of the response amplitude of a lightly damped linear oscillator driven by an evolutionary random excitation.

DISPERSIVE GROUNDWATER FLOW AND POLLUTION

1991 ◽  
Vol 01 (01) ◽  
pp. 61-81 ◽  
Author(s):  
ONNO A. VAN HERWAARDEN ◽  
JOHAN GRASMAN
Keyword(s):  
Random Walk ◽  
Dirichlet Problem ◽  
Groundwater Flow ◽  
Arrival Time ◽  
Kolmogorov Equation ◽  
Dispersive Flow ◽  
Backward Kolmogorov Equation ◽  
Protected Zone

By solving asymptotically the Dirichlet problem for the backward Kolmogorov equation describing the random walk of a particle in a dispersive flow, it is computed at what rate contaminated particles cross the boundary of a protected zone. The method also yields an estimate of the expected arrival time.

scholarly journals Chains of three-dimensional evolution algebras: A description

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3175-3190
Author(s):  
Anvar Imomkulov ◽  
Victoria Velasco
Keyword(s):  
Three Dimensional ◽  
Time Dependent ◽  
Kolmogorov Equation ◽  
Natural Basis ◽  
3 Dimensional ◽  
Evolution Algebra ◽  
Fixed Rank ◽  
Weighted Digraph

In this paper we describe locally all the chains of three-dimensional evolution algebras (3-dimensional CEAs). These are families of evolution algebras with the property that their structure matrices with respect to a certain natural basis satisfy the Chapman-Kolmogorov equation. We do it by describing all 3-dimensional CEAs whose structure matrices have a fixed rank equal to 3, 2 and 1, respectively. We show that arbitrary CEAs are locally CEAs of fixed rank. Since every evolution algebra can be regarded as a weighted digraph, this allows us to understand and visualize time-dependent weighted digraphs with 3 nodes.

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