An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics

10.1142/2183 ◽  
1994 ◽  
Author(s):  
Horacio S Wio
Keyword(s):  
Stochastic Processes ◽  
Statistical Physics ◽  
Nonequilibrium Statistical Physics

Introductory remarks

1990 ◽  
Vol 332 (1627) ◽  
pp. 417-418
Keyword(s):  
Probability Theory ◽  
Brownian Motion ◽  
Random Walk ◽  
Stochastic Processes ◽  
Statistical Physics ◽  
Late 19Th Century ◽  
Fields Of Study ◽  
Wide Range ◽  
Influential Paper ◽  
Telephone Traffic

Stochastic processes are systems that evolve in time probabilistically; their study is the ‘dynamics’ of probability theory as contrasted with rather more traditional ‘static’ problems. The analysis of stochastic processes has as one of its main origins late 19th century statistical physics leading in particular to studies of random walk and brownian motion (Rayleigh 1880; Einstein 1906) and via them to the very influential paper of Chandrasekhar (1943). Other strands emerge from the work of Erlang (1909) on congestion in telephone traffic and from the investigations of the early mathematical epidemiologists and actuarial scientists. There is by now a massive general theory and a wide range of special processes arising from applications in many fields of study, including those mentioned above. A relatively small part of the above work concerns techniques for the analysis of empirical data arising from such systems.

scholarly journals Spectral analysis for a class of integral-difference operators: known facts, new results, and open problems

2004 ◽  
Vol 2004 (1) ◽  
pp. 221-249 ◽  
Author(s):  
Yuri B. Melnikov
Keyword(s):  
Spectral Analysis ◽  
Present State ◽  
Statistical Physics ◽  
State Of The Art ◽  
Difference Operators ◽  
Open Problems ◽  
Nonequilibrium Statistical Physics

We present state of the art, the new results, and discuss open problems in the field of spectral analysis for a class of integral-difference operators appearing in some nonequilibrium statistical physics models as collision operators. The author dedicates this work to the memory of Professor Ilya Prigogine, who initiated this activity in 1997 and whose interesting and most enlightening advices had gudided the author during all these years.

Multiplicative stochastic processes in statistical physics

1979 ◽  
Vol 69 (5) ◽  
pp. 313-315 ◽  
Author(s):  
A. Schenzle ◽  
H. Brand
Keyword(s):  
Stochastic Processes ◽  
Statistical Physics
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