Martingale Problems Associated with the Boltzmann Equation

The Boltzmann equation is a nonlinear integro-partial differential equation that is supposed to describe the distribution of positions and velocities of the molecules in a dilute gas as a function of time. It is assumed that only two molecules at a time can collide.

[1]  F. Grünbaum,et al.  Propagation of chaos for the Boltzmann equation , 1971 .

[2]  A. Sznitman.  Équations de type de Boltzmann, spatialement homogènes , 1984 .

[3]  T. Funaki.  The diffusion approximation of the spatially homogeneous Boltzmann equation , 1985 .

[4]  Hiroshi Tanaka,et al.  Some probabilistic problems in the spatially homogeneous Boltzmann equation , 1983 .

[5]  T. Funaki.  The Diffusion Approximation of the Boltzmann Equation of Maxwellian Molecules , 1983 .

[6]  Hiroshi Tanaka.  Probabilistic treatment of the Boltzmann equation of Maxwellian molecules , 1978 .

[7]  Richard F. Bass,et al.  Uniqueness in law for pure jump Markov processes , 1988 .

[8]  Hiroshi Tanaka.  Stochastic differential equation corresponding to the spatially homogeneous Boltzmann equation of Maxwellian and non-cutoff type , 1987 .

[9]  D. W. Stroock,et al.  Multidimensional Diffusion Processes , 1979 .

[10]  M. Hp.  A class of markov processes associated with nonlinear parabolic equations. , 1966 .

[11]  K. Oelschlager.  A Martingale Approach to the Law of Large Numbers for Weakly Interacting Stochastic Processes , 1984 .

[12]  J. Jacod.  Calcul stochastique et problèmes de martingales , 1979 .

[13]  Tadahisa Funaki,et al.  A certain class of diffusion processes associated with nonlinear parabolic equations , 1984 .

[14]  K. Uchiyama.  Derivation of the Boltzmann equation from particle dynamics , 1988 .

[15]  M. Kac.  Foundations of Kinetic Theory , 1956 .

[16]  Daniel W. Stroock,et al.  Diffusion processes associated with Lévy generators , 1975 .

[17]  P. Echeverría.  A criterion for invariant measures of markov processes , 1982 .

[18]  Takashi Komatsu.  On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations of jump type , 1982 .

[19]  Clifford Ambrose Truesdell,et al.  Fundamentals of Maxwell's kinetic theory of a simple monatomic gas , 1980 .

[20]  Colin J. Thompson,et al.  Mathematical Statistical Mechanics , 1972 .

[21]  C. Cercignani.  The Boltzmann equation and its applications , 1988 .