Diffusion processes on graphs: stochastic differential equations, large deviation principle

[1]  B. Hajek,et al.  On large deviations in load sharing networks , 1998 .

[2]  B. Hajek,et al.  On large deviations of Markov processes with discontinuous statistics , 1998 .

[3]  M. Freidlin,et al.  On a Stochastic Model for Moisture Budget in an Eulerian Atmospheric Column , 1997 .

[4]  H. McKean,et al.  Diffusion processes and their sample paths , 1996 .

[5]  Mark Freidlin,et al.  Markov Processes and Di+erential Equations: Asymptotic Problems , 1996 .

[6]  P. Dupuis,et al.  The large deviation principle for a general class of queueing systems. I , 1995 .

[7]  A. Friedman,et al.  Diffusion in network , 1994 .

[8]  Mark Freidlin,et al.  Diffusion Processes on Graphs and the Averaging Principle , 1993 .

[9]  Sergei Leonov,et al.  Action functional for diffusions in discontinuous media , 1993 .

[10]  Tatsuya Okada,et al.  Asymptotic Behavior of Skew Conditional Heat Kernels on Graph Networks , 1993, Canadian Journal of Mathematics.

[11]  Joachim von Below,et al.  Classical solvability of linear parabolic equations on networks , 1988 .

[12]  Stephen D. Durham,et al.  Random motion on binary trees , 1984, Journal of Applied Probability.

[13]  L. Rogers.  Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00 , 1982 .

[14]  J. Harrison,et al.  On Skew Brownian Motion , 1981 .

[15]  Srinivasa Varadhan,et al.  Lectures on Diffusion Problems and Partial Differential Equations , 1980 .

[16]  T. Chiang,et al.  Large deviation of small perturbation of some unstable systems , 1997 .

[17]  Mark Freidlin,et al.  Random perturbations of Hamiltonian systems , 1994 .

[18]  R. L. Dobrushin,et al.  Process Level Large Deviations for a Class of Piecewise Homogeneous Random Walks , 1994 .

[19]  S. Leonov,et al.  Action functional for diffusion process with discontiuous drift , 1991 .

[20]  Jim Pitman,et al.  On Walsh's Brownian motions , 1989 .

[21]  S. Nicaise.  Some results on spectral theory over networks, applied to nerve impulse transmission , 1985 .

[22]  S. Varadhan.  Large Deviations and Applications , 1984 .

[23]  G. Lumer.  Connecting of local operators and evolution equations on networks , 1980 .

[24]  Shintaro Nakao,et al.  On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations , 1972 .