This work is devoted to stability of regime-switching diffusion processes. After presenting the formulation of regime-switching diffusions, the notion of stability is recalled, and necessary conditions for p-stability are obtained. Then main results on stability and instability for systems...

We provide a method for solving dynamic expected utility maximization problems with possibly not everywhere increasing utility functions in an Lp-semimartingale setting. In particular, we solve the problem for utility functions of type (exponential problem) and (2m-th problem). The convergence...

We study the probability that chordal in the unit disk from to 1 avoids the disk of radius q centered at zero. We find the initial/boundary value problem satisfied by this probability as a function of x and a=lnq, and show that asymptotically as q tends to 1 this probability decays like...

We consider the [alpha]-stable Ornstein-Uhlenbeck process as a solution of the Langevin equation where the Brownian motion is replaced by an isotropic [alpha]-stable process. We give sharp estimates for the expectation of the first exit time from the center of a ball B(x,r) for all and r0. We...

We consider asymptotic properties of curve-crossing counts of linear processes and nonlinear time series by curves. Central limit theorems are obtained for curve-crossing counts of short-range dependent processes. For the long-range dependence case, the asymptotic distributions are shown to be...

Doukhan and Louhichi [P. Doukhan, S. Louhichi, A new weak dependence condition and application to moment inequalities, Stochastic Process. Appl. 84 (1999) 313-342] introduced a new concept of weak dependence which is more general than mixing. Such conditions are particularly well suited for...

The addition of a Bessel drift to a Brownian motion affects the lifetime of the process in the interval (0,[infinity]) in a well-understood way. We study the corresponding effect of a power of the Bessel drift. The most interesting case occurs when [beta]0. If p1 then the effect of the drift is...

We study the error induced by the time discretization of decoupled forward-backward stochastic differential equations (X,Y,Z). The forward component X is the solution of a Brownian stochastic differential equation and is approximated by a Euler scheme XN with N time steps. The backward component...

Let be an i.i.d. random field of square integrable centered random elements in the separable Hilbert space and , , be the summation processes based on the collection of sets [0,t1]x...x[0,td], 0<=ti<=1, i=1,...,d. When d>=2, we characterize the weak convergence of in the Hölder space by the finiteness of the weak p...</=ti<=1,>

A suitable canonical Lévy process is constructed in order to study a Malliavin calculus based on a chaotic representation property of Lévy processes proved by Itô using multiple two-parameter integrals. In this setup, the two-parameter derivative Dt,x is studied, depending on whether x=0 or...