Matyas Barczy

Asymptotic behavior of unstable INAR(p) processes

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unstable autoregressive processes of order p. An application for Boston armed robberies data set is presented.

Karhunen-Loève expansions of α-Wiener bridges

AbstractWe study Karhunen-Loève expansions of the process(Xt(α))t∈[0,T) given by the stochastic differential equation % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX % garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy % Ubqee0evGueE0jxyaibaieYdh9Lrpeeu0dXdh9vqqj-hEeeu0xXdbb % a9frpm0db9Lqpepeea0xd9q8as0-LqLs-Jirpepeea0-as0Fb9pgea % 0lrP0xe9Fve9Fve9qapdbaqaaeGaciGaaiaabeqaamaaeaqbaaGcba % acbaGaa8hzaiacyc4GybWaiGjGDaaaleacycOaiGjGdshaaeacycOa % iGjGcIcacWaMasySdeMaiGjGcMcaaaGccWaMaAypa0JamGjGgkHiTm % acyc4caaqaiGjGcWaMasySdegabGaMakacyc4GubGamGjGgkHiTiac % yc4G0baaaiacyc4GybWaiGjGDaaaleacycOaiGjGdshaaeacycOaiG % jGcIcacWaMasySdeMaiGjGcMcaaaGccGaSa+hzaiac8c4G0bGamWlG % gUcaRiac8c4FKbGaiGmGdkeadGaYaUbaaSqaiGmGcGaYaoiDaaqajG % mGaOGaiGmGcYcacGaGaInaaaWG0bGamaiGydaaayicI4SaiaiGydaa % ai4waiacaci2aaaaicdacGaGaInaaaGGSaGaiaiGydaaamivaiacac % i2aaaacMcaaaa!8F89!

On parameter estimation for critical affine processes

dX_t^{(\alpha )} = - \frac{\alpha } {{T - t}}X_t^{(\alpha )} dt + dB_t ,t \in [0,T)

Linear maps on the space of all bounded observables preserving maximal deviation

, with the initial condition X0(α) = 0, where α > 0, T ∈ (0, ∞), and (Bt)t≥0 is a standard Wiener process. This process is called an α-Wiener bridge or a scaled Brownian bridge, and in the special case of α = 1 the usual Wiener bridge. We present weighted and unweighted Karhunen-Loève expansions of X(α). As applications, we calculate the Laplace transform and the distribution function of the L2[0, T]-norm square of X(α) studying also its asymptotic behavior (large and small deviation).

Asymptotic properties of maximum-likelihood estimators for Heston models based on continuous time observations

We study the existence of a unique stationary distribution and ergodicity for a two-dimensional affine process. Its first coordinate process is supposed to be a so-called α-root process with α ∈ (1, 2]. We prove the existence of a unique stationary distribution for the affine process in the α ∈ (1, 2] case; furthermore, we show ergodicity in the α = 2 case.

Yamada-Watanabe Results for Stochastic Differential Equations with Jumps

First we provide a simple set of sufficient conditions for the weak convergence of scaled affine processes with state space

Asymptotic behavior of critical, irreducible multi-type continuous state and continuous time branching processes with immigration

R_+ \times R^d

Representations of multidimensional linear process bridges

. We specialize our result to one-dimensional continuous state branching processes with immigration. As an application, we study the asymptotic behavior of least squares estimators of some parameters of a two-dimensional critical affine diffusion process.