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What do card shuffling, volume growth, and Harnack inequalities have to do with each other? They all arise in the study of random walks on groups. Probability on groups is concerned with probabil...
Let Ω ⊂ Rn be a bounded domain and for x ∈ Ω let τ(x) be the expected exit time from Ω of a diffusing particle starting at x and advected by an incompressible flow u. We are in...
We consider a multidimensional diffusion X with drift coefficient b({\alpha},X(t)) and diffusion coefficient {\epsilon}{\sigma}({\beta},X(t)). The diffusion is discretely observed at times t_k=k{\Delt...
We provide a complete characterization of the class of one-dimensional time-homogeneous diffusions consistent with a given law at an exponentially distributed time using classical results in diffusion...
Abstract: We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these probl...
Abstract: We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obta...
Abstract: The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noise asymptotics for invariant densities for a class of diffusions: a control theoretic view, J. Math. Anal. and Appl. (...
Abstract: We address the question of the trends to equilibrium for a large class C of relativistic diffusions. We show the existence of a spectral gap using the Lyapounov method and deduce the exponen...
We observe that some special Itˆo diffusions are related to scattering properties of a Schr¨odinger operator on Rd, d  2. We introduce Feynman-Kac type formulae for these stochastic processes wh...
We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control pro...
Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing th...
We prove the transportation inequality with the uniform norm for the laws of diffusion pro- cesses with Lipschitz and/or dissipative coefficients and apply them to some singular stochastic differenti...
We develop a specification test for the transition density of a discretely sampled continuous-time jump-diffusion process, based on a comparison of a nonparametric estimate of the transition density o...
A class of hybrid jump diffusions modulated by a Markovchain is considered in this work. The motivation stems frominsurance risk models, and emerging applications in productionplanning and wireless co...
Using the method of Girsanovtransformation, we establish the Talagrand's $T_2$-inequality fordiffusion on the path space $C([0,N], \rr^d)$ with respect to auniform metric, with the constant independen...

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