In this paper we give a characterization of minimal distance martingale measures with respect to f-divergence distances in a general semimartin-gale market model. We provide necessary and suucient conditions for minimal distance martingale measures and determine them explicitly for exponential L evy processes with respect to several classical distances. It is shown that the minimal distance mar...

The paper develops multiplicative compensation for complex-valued semimartingales and studies some of its consequences. It is shown that the stochastic exponential any semimartingale with independent increments becomes a true martingale after when such meaningful. This generalization L\'evy--Khintchin formula fills an existing gap in literature. allows, example, computation Mellin transform sig...

A continuous-time particle system on the real line satisfying branching property and an exponential integrability condition is called a L\'evy process, its law characterized by triplet $(\sigma^2,a,\Lambda)$. We obtain necessary sufficient for convergence of derivative martingale such process to non-trivial limit in terms This extends previously known results Brownian motions random walks. To t...

We use Dirichlet form methods to construct and analyse a general class of reversible Markov processes with totally disconnected state spaces. We study in detail the special case of bipartiteMarkov chains. The latter processes have a state space consisting of an \interior" with a countable number of isolated points and a, typically uncountable, \boundary". The equilibrium measure assigns all of ...

The escape from a given domain is one of the fundamental problems in statistical physics and theory stochastic processes. Here, we explore properties an inertial particle driven by L\'evy noise bounded domain, restricted two absorbing boundaries.Presence boundaries assures that process can be characterized finite mean first passage time. detailed analysis kinetics shows time for integrated Orns...

Multiple scattering of light by resonant vapor is characterized L\'evy-type superdiffusion with a single-step size distribution $p(x)\ensuremath{\propto}1/{x}^{1+\ensuremath{\alpha}}$. We investigate L\'evy flight in hot rubidium collisional-broadened 50 torr He gas. The frequent collisions produce Lorentzian absorptive and emissive profiles $\ensuremath{\alpha}<1$ corresponding divergent me...

We introduce a type assignment system which is parametric with respect to ve families of trees obtained by evaluating -terms (Bohm trees, L evy-Longo trees, ...). Then we prove, in an (almost) uniform way, that each type assignment system fully describes the observational equivalences induced by the corresponding tree representation of terms. More precisely, for each family of trees two terms ...