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A simulation of integral and derivative of the solution of a stochastici integral equation

Nguyen Quy Hy, Nguyen Thi Minh (1992)

Annales Polonici Mathematici

A stochastic integral equation corresponding to a probability space ( Ω , Σ ω , P ω ) is considered. This equation plays the role of a dynamical system in many problems of stochastic control with the control variable u ( · ) : ℝ 1 → ℝ m . One constructs stochastic processes η ( 1 ) ( t ) , η ( 2 ) ( t ) connected with a Markov chain and with the space ( Ω , Σ ω , P ω ) . The expected values of η ( i ) ( t ) (i = 1,2) are respectively the expected value of an integral representation of a solution x(t) of the equation and that of its derivative x u ' ( t ) .

A stability theorem for elliptic Harnack inequalities

Richard F. Bass (2013)

Journal of the European Mathematical Society

We prove a stability theorem for the elliptic Harnack inequality: if two weighted graphs are equivalent, then the elliptic Harnack inequality holds for harmonic functions with respect to one of the graphs if and only if it holds for harmonic functions with respect to the other graph. As part of the proof, we give a characterization of the elliptic Harnack inequality.

A stationary random graph of no growth rate

Ádám Timár (2014)

Annales de l'I.H.P. Probabilités et statistiques

We present a random automorphism-invariant subgraph of a Cayley graph such that with probability 1 its exponential growth rate does not exist.

A stochastic approach to relativistic diffusions

Ismaël Bailleul (2010)

Annales de l'I.H.P. Probabilités et statistiques

A new class of relativistic diffusions encompassing all the previously studied examples has recently been introduced in the article of C. Chevalier and F. Debbasch (J. Math. Phys. 49 (2008) 043303), both in a heuristic and analytic way. A stochastic approach of these processes is proposed here, in the general framework of lorentzian geometry. In considering the dynamics of the random motion in strongly causal spacetimes, we are able to give a simple definition of the one-particle distribution function...

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