Probability and Stochastic Processes

This essay needs an apology rather than a preface. It is an attempt to present to the physicist a physical approach to the theory of stochastic processes, a field till recently the close preserve of the mathematician. The only justification for the style and form adopted here lies in that the theory of stochastic processes as formulated in abstract mathematical treatises and papers is difficult to read even to those who are trained to a rigorous mathematical discipline. But in many problems where some random element is introduced, the physicist needs a knowledge of the results of stochastic theory and he would like to use them without being diverted by mathematical details or trammelled by the demands of rigour. Such examples are cited, but no pretence is made to completeness, and the emphasis is laid only on the methods used in applying a general theory to particular problems.

[1]  T. E. Harris,et al.  On the Theory of Age-Dependent Stochastic Branching Processes. , 1948, Proceedings of the National Academy of Sciences of the United States of America.

[2]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[3]  J. Uspensky.  Introduction to mathematical probability , 1938 .

[4]  C. J. Tranter,et al.  Integral Transforms in Mathematical Physics , 1952 .

[5]  R. Feynman,et al.  Space-Time Approach to Non-Relativistic Quantum Mechanics , 1948 .

[6]  R Kalaba,et al.  ON THE PRINCIPLE OF INVARIANT IMBEDDING AND ONE-DIMENSIONAL NEUTRON MULTIPLICATION. , 1957, Proceedings of the National Academy of Sciences of the United States of America.

[7]  S. Chandrasekhar.  Stochastic problems in Physics and Astronomy , 1943 .

[8]  W. Heitler,et al.  The quantum theory of radiation , 1936 .

[9]  W. H. Furry.  On Fluctuation Phenomena in the Passage of High Energy Electrons through Lead , 1937 .

[10]  Alladi Ramakrishnan.  A physical approach to stochastic processes , 1956 .

[11]  R. Feynman.  An Operator calculus having applications in quantum electrodynamics , 1951 .

[12]  M. S. Bartlett,et al.  Recurrence and first passage times , 1953, Mathematical Proceedings of the Cambridge Philosophical Society.

[13]  Ordinary linear differential equations involving random functions , 1956 .

[14]  A. Kolmogoroff.  Grundbegriffe der Wahrscheinlichkeitsrechnung , 1933 .

[15]  L. Jánossy,et al.  Fluctuations of the Electron-Photon Cascade - Moments of the Distribution , 1950 .

[16]  Max Born,et al.  A general kinetic theory of liquids , 1949 .

[17]  J. Doob.  Stochastic processes , 1953 .

[18]  A. Khinchin.  Mathematical foundations of statistical mechanics , 1949 .

[19]  A. Ramakrishnan.  A note on Janossy's mathematical model of a nucleon cascade , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[20]  M. S. Bartlett,et al.  On the use of the characteristic functional in the analysis of some stochastic processes occurring in physics and biology , 1951, Mathematical Proceedings of the Cambridge Philosophical Society.

[21]  N. Wiener.  Generalized harmonic analysis , 1930 .

[22]  D. Kendall,et al.  On some modes of population growth leading to R. A. Fisher's logarithmic series distribution. , 1948, Biometrika.

[23]  A. Ramakrishnan.  Inverse probability and evolutionary markoff stochastic processes , 1955 .

[24]  Zevi W. Salsburg,et al.  Molecular Distribution Functions in a One‐Dimensional Fluid , 1953 .

[25]  M. Bartlett,et al.  On the asymptotic probability distribution for certain Markoff processes , 1950, Mathematical Proceedings of the Cambridge Philosophical Society.

[26]  Alladi Ramakrishnan,et al.  Stochastic processes relating to particles distributed in a continuous infinity of states , 1950, Mathematical Proceedings of the Cambridge Philosophical Society.

[27]  F. Dyson.  The S Matrix in Quantum Electrodynamics , 1949 .