This paper considers estimation of the function g in the model Yt = g(Xt) + εt when E(εt|Xt) 6= 0 with non–zero probability. We assume the existence of an ‘instrumental variable’ Zt that is independent of εt and of an ‘innovation’ ηt = Xt − E(Xt|Zt). We use a nonparametric regression of Xt on Zt to obtain residuals η̂t which in turn are used to obtain a consistent estimator of g. The estimator w...

A locating-dominating set of an undirected graph is a subset vertices S such that dominating and for every u,v?S, the neighbourhood u v on are distinct (i.e. N(u)?S?N(v)?S). Locating-dominating sets have received considerable attention in last decades. In this paper, we consider oriented version problem. each w?V?S, N?(w)?S?? pair u,v?V?S, N?(u)?S?N?(v)?S. We following two parameters. Given G, ...

We develop numerical methods for computing statistics of stochastic processes on surfaces general shape with drift-diffusion dynamics dXt=a(Xt)dt+b(Xt)dWt. formulate descriptions Brownian motion and surfaces. consider the form u(x)=Ex[∫0τg(Xt)dt]+Ex[f(Xτ)] a domain Ω exit stopping time τ=inft⁡{t>0|Xt∉Ω}, where f,g are smooth functions. For these statistics, we high-order Generalized Moving Leas...

dXt dt = f(Xt, t)dt+ g(Xt, t)dWt (1) where Xt = X(t) is the realization of a stochastic process or random variable. f(Xt, t) is called the drift coefficient, that is the deterministic part of the SDE characterizing the local trend. g(Xt, t) denotes the diffusion coefficient, that is the stochastic part which influences the average size of the fluctuations of X. The fluctuations themselves origi...

in Euclidean spaces, with Fn(x, a ) and Gn(x) converging pointwise to functions F,(x,a) and G,(x), respectively, and give conditions for the limiting P O model Xt+l = F,(xt,at) + t t , Yt = G,(xt) + rlt to have an a-discount optimal policy. AMS Classification: 93320, 90C40.

Let V and W be vector spaces of dimension m and n resp. We investigate the Zariski closure Xt of the image Yt of the map HomK(V,W ) → HomK( ∧t V, ∧t W ), φ 7→ ∧t φ . In the case t = min(m,n), Yt = Xt is the cone over a Grassmannian, but for 1 < t < min(m,n) one has Xt 6= Yt . We analyze the G = GL(V )×GL(W )-orbits in Xt via the G-stable prime ideals in O(Xt). It turns out that they are classif...

Let v : [0, T ] × R → R be the solution of the parabolic backward equation ∂tv + (1/2) ∑ i,j [σσ ]i,j∂xi∂xjv + ∑ i bi∂xiv + kv = 0 with terminal condition g, where the coefficients are timeand state-dependent, and satisfy certain regularity assumptions. Let X = (Xt)t∈[0,T ] be the associated R -valued diffusion process on some appropriate (Ω,F ,Q). For p ∈ [2,∞) and a measure dP = λT dQ, where ...

Let P0 denote the Wiener measure defined on the canonical space ( Ω = C(R+,R), (Xt)t≥0, (Ft)t≥0 ) , and (St) (resp. (It)), be the one sided-maximum (resp. minimum), (L 0 t ) the local time at 0, and (Dt) the number of down-crossings from b to a (with b > a). Let f : R×Rd −→]0,+∞[ be a Borel function, and (At) be a process chosen within the set : { (St); (St, t); (L 0 t ); (St, It, L 0 t ); (Dt)...

These types of functionals have numerous applications. For example, if λ= 0, g(x) = x, then the expectation gives the price of a zero coupon bond in financial mathematics. If g(Xt) = μh(Xt) and h(Xt) does not depend on μ, then the expectation is the two dimensional Laplace transform of the joint density of (Xt, ∫ t 0 h(Xs)ds). Most cases must be handled numerically, but recently considerable at...

We prove necessary and sufficient conditions for the almost sure convergence of the integrals ∫∞ 1 g(a(t)+Mt)df(t), ∫ 1 0 g(a(t)+Mt)df(t), and thus of ∫∞ 0 g(a(t)+Mt)df(t), where Mt = sup{|Xs| : s ≤ t} is the two-sided maximum process corresponding to a Lévy process (Xt)t≥0, a(·) is a nondecreasing function on [0,∞) with a(0) = 0, g(·) is a positive nonincreasing function on (0,∞), possibly wit...