Introducing certain singularities, we generalize the class of one-dimensional stochastic differential equations with so-called generalized drift. Equations with generalized drift, well-known in the literature, possess a drift that is described by the semimartingale local time of the unknown...

We consider the finite capacity M/M/1−K queue with a time dependent arrival rate λ(t). Assuming that the capacity K is large and that the arrival rate varies slowly with time (as t/K), we construct asymptotic approximations to the probability of finding n customers in the system at time t, as...

We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary (gij(t,x)≥0). We show existence of the optimal strategy, via a verification theorem. Finally, when the state of the system is a Markov...

The truncated variation, TVc, is a fairly new concept introduced in Łochowski (2008) [5]. Roughly speaking, given a càdlàg function f, its truncated variation is “the total variation which does not pay attention to small changes of f, below some threshold c0”. The very basic consequence...

In a recent paper, Soner, Touzi and Zhang (2012) [19] have introduced a notion of second order backward stochastic differential equations (2BSDEs), which are naturally linked to a class of fully non-linear PDEs. They proved existence and uniqueness for a generator which is uniformly Lipschitz in...

We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coëfficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic collision, to perfect reflection of one particle on the other....

We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings for Lévy processes obtained essentially via the...

Let ξ=(ξt) be a locally finite (2,β)-superprocess in Rd with β<1 and d>2/β. Then for any fixed t0, the random measure ξt can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the ε-neighborhoods of suppξt. This extends the Lebesgue approximation of Dawson–Watanabe...</1>

We consider large time behaviour of typical paths under the Anderson polymer measure. If Pκx is the measure induced by rate κ, simple, symmetric random walk on Zd started at x, this measure is defined as dμκ,β,Tx(X)=Zκ,β,T(x)−1exp{β∫0TdWX(s)(s)}dPκx(X) where {Wx:x∈Zd} is a field...

We prove regularity estimates for functions which are harmonic with respect to certain jump processes. The aim of this article is to extend the method of Bass–Levin (2002) [3] and Bogdan–Sztonyk (2005) [6] to more general processes. Furthermore, we establish a new version of the Harnack...