A simple and robust approach is proposed for the parametric estimation of scalar homogeneous stochastic di¤erential equations. We specify a parametric class of di¤usions and estimate the parameters of interest by minimizing criteria based on the integrated squared di¤erence between kernel estimates of the drift and di¤usion functions and their parametric counterparts. The procedure does not req...

In this Note we present new results which bring about hitherto unknown relations between certain Bernstein di¤usions wandering in bounded convex domains of Euclidean space on the one hand, and processes which typically occur in forward-backward systems of stochastic di¤erential equations on the other hand. A key point in establishing such relations is the fact that the Bernstein di¤usions we co...

In the running of a genetic algorithm, the population is liable to be con ned in the local optimum, that is the metastable state, making an equilibrium. It is known that, after a long time, the equilibrium is punctuated suddenly and the population transits into the better neighbor optimum. We adopt the formalization of Computational Ecosystems to show that the dynamics of the Simple Genetic Alg...

The existence of an adapted solution to a backward stochastic differential equation which is not adapted to the ltration of the underlying Brownian motion is proved. This result is applied to the pricing of contingent claims. It allows to compare the prices of agents who have di erent information about the evolution of the market. The problem is considered in both the classical and the F ollme...

In this paper we address the problem of characterizing the in nitesimal properties of functions which are non-increasing along all the trajectories of a di erential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous di erential inclusions. Moreover, we show that the same criterion applies also in the ...

We study oscillatory behavior of a class of second-order neutral di¤erential equations relating oscillation of these equations to existence of positive solutions to associated first-order functional di¤erential inequalities. Our assumptions allow applications to di¤erential equations with both delayed and advanced arguments, and not only. New theorems complement and improve a number of results ...

in this study, a new and ecient approach is presented for numerical solution offredholm integro-dierential equations (fides) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized laguerrepolynomials(glps). properties of these polynomials and operational matrices of integration,dierentiation are introduced and are ultilized to r...

We study large deviation properties of systems of weakly interacting particles modeled by Itô stochastic di erential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures converges, as the number of particles tends to in nity, to the weak solution of an associated McKean-Vlasov equation. We derive a large deviation principle via the weak co...

We present a Petri net formalism that allows for mixed discrete and continuous stochastic models. The continuous part of the models consists of uid places that are lled and emptied at random (normally distributed) rate. Fluid places can be used for the modelling of continuous system components as well as for continuous approximation of heavily loaded discrete places in order to avoid state spac...

In this paper we present an analytic treatment of the inverse problem of reconstructing the internal electric conductivity of an in nite domain (the lower half space) from electrical measurements performed on its surface. To this end we transform the initial di erential equation into an integral equation, a procedure which has the advantage of permitting a simple discussion of the regularizatio...