A general version of the fundamental theorem of asset pricing.
A generalization of entropy equation: homogeneous entropies
A generalized Biane process
A generalized Chacon's inequality and order convergence of processes
A generalized fundamental identity
A generalized mean-reverting equation and applications
Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0,T] (T> 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability of the...
A geometric approach to on-diagonal heat kernel lower bounds on groups
We introduce a new method for obtaining heat kernel on-diagonal lower bounds on non- compact Lie groups and on infinite discrete groups. By using this method, we are able to recover the previously known results for unimodular amenable Lie groups as well as for certain classes of discrete groups including the polycyclic groups, and to give them a geometric interpretation. We also obtain new results for some discrete groups which admit the structure of a semi-direct product or of a wreath product....
A Green's Function for Non-Homogegeous Random Walks on Free Products.
A growth estimate for continuous random fields
We prove a polynomial growth estimate for random fields satisfying the Kolmogorov continuity test. As an application we are able to estimate the growth of the solution to the Cauchy problem for a stochastic diffusion equation.
A Hilbert transform for non-homogeneous martingales
A Hölderian FCLT for some multiparameter summation process of independent non-identically distributed random variables.
A joint limit theorem for compactly regenerative ergodic transformations
We study conservative ergodic infinite measure preserving transformations satisfying a compact regeneration property introduced by the second-named author in J. Anal. Math. 103 (2007). Assuming regular variation of the wandering rate, we clarify the asymptotic distributional behaviour of the random vector (Zₙ,Sₙ), where Zₙ and Sₙ are respectively the time of the last visit before time n to, and the occupation time of, a suitable set Y of finite measure.
A limit law for random walk in a random environment
A limit theorem for functionals of a Poisson process
A limit theorem for joint distribution of order-statistics from stationary Gaussian sequences
A limit theorem for maxima of nonstationary Gaussian sequences
A limit theorem for the prediction process under absolute continuity
A limiting distribution for quicksort
A linear programming approach to error bounds for random walks in the quarter-plane
We consider the steady-state behavior of random walks in the quarter-plane, in particular, the expected value of performance measures that are component-wise linear over the state space. Since the stationary distribution of a random walk is in general not readily available we establish upper and lower bounds on performance in terms of another random walk with perturbed transition probabilities, for which the stationary distribution is a geometric product-form. The Markov reward approach as developed...
A Local Limit Theorem on the Semi-Direct Product of and