Expansions in Statistical Mechanics as Part of the Theory of Partial Differential Equations

1987 ◽  
pp. 31-47
Author(s):  
D. C. Brydges
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Statistical Mechanics ◽  
Partial Differential

Moments of age and remaining life in renewal processes

1973 ◽  
Vol 10 (02) ◽  
pp. 307-316
Author(s):  
S. Katz ◽  
P. Naor ◽  
R. Shinnar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Statistical Mechanics ◽  
Sequential Analysis ◽  
Renewal Theory ◽  
Independent Interest ◽  
Renewal Processes ◽  
Remaining Life ◽  
Analysis Framework ◽  
Partial Differential

Expressions are developed for the moments of age and remaining life in renewal processes, and from them, expressions for the moments of the last and next renewal epochs. The results for remaining life and next renewal epoch may be regarded as generalizations of theorems of Wald (1944) and others. The results for age and last renewal epoch do not fit into this sequential analysis framework. Both sets of results are obtained from partial differential equations developed for the distributions of age and of remaining life. These partial differential equations are of the “conservation” type familiar from statistical mechanics, and may have some independent interest for renewal theory.

Moments of age and remaining life in renewal processes

1973 ◽  
Vol 10 (2) ◽  
pp. 307-316
Author(s):  
S. Katz ◽  
P. Naor ◽  
R. Shinnar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Statistical Mechanics ◽  
Sequential Analysis ◽  
Renewal Theory ◽  
Independent Interest ◽  
Renewal Processes ◽  
Remaining Life ◽  
Analysis Framework ◽  
Partial Differential

Expressions are developed for the moments of age and remaining life in renewal processes, and from them, expressions for the moments of the last and next renewal epochs. The results for remaining life and next renewal epoch may be regarded as generalizations of theorems of Wald (1944) and others. The results for age and last renewal epoch do not fit into this sequential analysis framework. Both sets of results are obtained from partial differential equations developed for the distributions of age and of remaining life. These partial differential equations are of the “conservation” type familiar from statistical mechanics, and may have some independent interest for renewal theory.

Partial Differential Equations

2020 ◽  
Author(s):  
A. K. Nandakumaran ◽  
P. S. Datti
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential
Sign in / Sign up

Export Citation Format

Share Document